Unformatted Attachment Preview
CHAPTER 5
TIME VALUE OF MONEY
(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)
Note that there is some overlap between the T/F and the multiple choice questions, as some T/F
statements are used in the MC questions. See the preface for information on the AACSB letter
indicators (F, M, etc.) on the subject lines.
Multiple Choice: True/False
(5-2) Compounding
1.
F J
Answer: a
EASY
Starting to invest early for retirement increases the benefits of
compound interest.
a. True
b. False
(5-2) Compounding
2.
F J
Answer: b
EASY
Starting to invest early for retirement reduces the benefits of compound
interest.
a. True
b. False
(5-2) Compounding
3.
F J
Answer: a
EASY
A time line is meaningful even if all cash flows do not occur annually.
a. True
b. False
(5-2) Compounding
4.
F J
Answer: b
EASY
A time line is not meaningful unless all cash flows occur annually.
a. True
b. False
(5-2) Compounding
F J
Answer: a EASY
5.
Time lines can be constructed in situations where some of the cash flows
occur annually but others occur quarterly.
a. True
b. False
(5-2) Compounding
6.
F J
Answer: b
EASY
Time lines cannot be constructed in situations where some of the cash
flows occur annually but others occur quarterly.
a. True
b. False
Chapter 5: Time Value of Money
True/False
Page 135
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-2) Compounding
7.
F J
Answer: a
EASY
Time lines can be constructed for annuities where the payments occur at
either the beginning or the end of the periods.
a. True
b. False
(5-2) Compounding
8.
F J
Answer: b
EASY
Time lines cannot be constructed for annuities unless all the payments
occur at the end of the periods.
a. True
b. False
(5-2) Compounding
9.
F J
Answer: a
EASY
Some of the cash flows shown on a time line can be in the form of
annuity payments while others can be uneven amounts.
a. True
b. False
(5-2) Compounding
10.
F J
Answer: b
EASY
Some of the cash flows shown on a time line can be in the form of
annuity payments but none can be uneven amounts.
a. True
b. False
(5-3) PV versus FV
11.
C J
Answer: b
EASY
If the discount (or interest) rate is positive, the present value of an
expected series of payments will always exceed the future value of the
same series.
a. True
b. False
(5-3) PV versus FV
12.
C J
Answer: a
EASY
If the discount (or interest) rate is positive, the future value of an
expected series of payments will always exceed the present value of the
same series.
a. True
b. False
(5-3) PV versus FV
13.
C J
Answer: a
EASY
Disregarding risk, if money has time value, it is impossible for the
present value of a given sum to exceed its future value.
a. True
b. False
Page 136
True/False
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-3) PV versus FV
14.
C J
Answer: b
EASY
Disregarding risk, if money has time value, it is impossible for the
future value of a given sum to exceed its present value.
a. True
b. False
(5-16) Effective annual rate
15.
C J
Answer: b
EASY
If a bank compounds savings accounts quarterly, the nominal rate will
exceed the effective annual rate.
a. True
b. False
(5-16) Effective annual rate
16.
C J
Answer: a
EASY
If a bank compounds savings accounts quarterly, the effective annual
rate will exceed the nominal rate.
a. True
b. False
(5-2) Compounding
17.
C J
Answer: b
MEDIUM
The greater the number of compounding periods within a year, then (1)
the greater the future value of a lump sum investment at Time 0 and (2)
the greater the present value of a given lump sum to be received at some
future date.
a. True
b. False
(5-2) Compounding
18.
C J
Answer: a
MEDIUM
The greater the number of compounding periods within a year, then (1)
the greater the future value of a lump sum investment at Time 0 and (2)
the smaller the present value of a given lump sum to be received at some
future date.
a. True
b. False
(5-2) Comparative compounding
19.
C J
Answer: a
MEDIUM
Suppose Sally Smith plans to invest $1,000. She can earn an effective
annual rate of 5% on Security A, while Security B has an effective
annual rate of 12%. After 11 years, the compounded value of Security B
should be more than twice the compounded value of Security A. (Ignore
risk, and assume that compounding occurs annually.)
a. True
b. False
Chapter 5: Time Value of Money
True/False
Page 137
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-2) Comparative compounding
20.
C J
Answer: b
MEDIUM
Suppose Randy Jones plans to invest $1,000. He can earn an effective
annual rate of 5% on Security A, while Security B has an effective
annual rate of 12%. After 11 years, the compounded value of Security B
should be somewhat less than twice the compounded value of Security A.
(Ignore risk, and assume that compounding occurs annually.)
a. True
b. False
(5-3) PV of a sum
21.
C J
Answer: a
MEDIUM
The present value of a future sum decreases as either the discount rate
or the number of periods per year increases, other things held constant.
a. True
b. False
(5-3) PV of a sum
22.
C J
Answer: b
MEDIUM
The present value of a future sum increases as either the discount rate
or the number of periods per year increases, other things held constant.
a. True
b. False
(5-9) PV of an annuity
23.
C J
Answer: a
MEDIUM
All other things held constant, the present value of a given annual
annuity decreases as the number of periods per year increases.
a. True
b. False
(5-9) PV of an annuity
24.
C J
Answer: b
MEDIUM
All other things held constant, the present value of a given annual
annuity increases as the number of periods per year increases.
a. True
b. False
(5-15) Periodic and nominal rates
25.
C J
Answer: a
MEDIUM
If we are given a periodic interest rate, say a monthly rate, we can
find the nominal annual rate by multiplying the periodic rate by the
number of periods per year.
a. True
b. False
(5-15) Periodic and nominal rates
26.
C J
Answer: b
MEDIUM
If we are given a periodic interest rate, say a monthly rate, we can
find the nominal annual rate by dividing the periodic rate by the number
of periods per year.
a. True
b. False
Page 138
True/False
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-16) Effective and nominal rates
27.
C J
Answer: a
MEDIUM
As a result of compounding, the effective annual rate on a bank deposit
(or a loan) is always equal to or greater than the nominal rate on the
deposit (or loan).
a. True
b. False
(5-16) Effective and nominal rates
28.
C J
Answer: b
MEDIUM
As a result of compounding, the effective annual rate on a bank deposit
(or a loan) is always equal to or less than the nominal rate on the
deposit (or loan).
a. True
b. False
(5-18) Amortization
29.
C J
Answer: b
MEDIUM
When a loan is amortized, a relatively high percentage of the payment
goes to reduce the outstanding principal in the early years, and the
principal repayment's percentage declines in the loan's later years.
a. True
b. False
(5-18) Amortization
30.
C J
Answer: a
MEDIUM
When a loan is amortized, a relatively low percentage of the payment
goes to reduce the outstanding principal in the early years, and the
principal repayment's percentage increases in the loan's later years.
a. True
b. False
(5-18) Amortization
31.
C J
Answer: a
MEDIUM
The payment made each period on an amortized loan is constant, and it
consists of some interest and some principal. The closer we are to the
end of the loan's life, the greater the percentage of the payment that
will be a repayment of principal.
a. True
b. False
(5-18) Amortization
32.
C J
Answer: b
MEDIUM
The payment made each period on an amortized loan is constant, and it
consists of some interest and some principal. The closer we are to the
end of the loan's life, the smaller the percentage of the payment that
will be a repayment of principal.
a. True
b. False
Chapter 5: Time Value of Money
True/False
Page 139
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-18) Amortization
33.
C J
Answer: b
HARD
Midway through the life of an amortized loan, the percentage of the
payment that represents interest must be equal to the percentage that
represents repayment of principal. This is true regardless of the
original life of the loan or the interest rate on the loan.
a. True
b. False
(5-18) Amortization
34.
C J
Answer: a
HARD
Midway through the life of an amortized loan, the percentage of the
payment that represents interest could be equal to, less than, or
greater than to the percentage that represents repayment of principal.
The proportions depend on the original life of the loan and the interest
rate.
a. True
b. False
Multiple Choice: Conceptual
The correct answers to most of these questions can be determined without doing any
calculations, but calculations are required for a few of them, and calculations are useful to
confirm the answers to others. You can see from the answer where calculations are required.
Those questions generally take students longer to answer.
(5-1) Time lines
35.
F J
Answer: b
MEDIUM
Which of the following statements is CORRECT?
a. A time line is not meaningful unless all cash flows occur annually.
b. Time lines are useful for visualizing complex problems prior to doing
actual calculations.
c. Time lines cannot be constructed in situations where some of the cash
flows occur annually but others occur quarterly.
d. Time lines cannot be constructed for annuities where the payments
occur at the beginning of the periods.
e. Some of the cash flows shown on a time line can be in the form of
annuity payments, but none can be uneven amounts.
(5-1) Time lines
36.
F J
Answer: d
MEDIUM
Which of the following statements is CORRECT?
a. A time line is not meaningful unless all cash flows occur annually.
b. Time lines are not useful for visualizing complex problems prior to
doing actual calculations.
c. Time lines cannot be constructed in situations where some of the cash
flows occur annually but others occur quarterly.
d. Time lines can be constructed for annuities where the payments occur
at either the beginning or the end of the periods.
e. Some of the cash flows shown on a time line can be in the form of
annuity payments, but none can be uneven amounts.
Page 140
Conceptual M/C
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-1) Time lines
37.
F J
Answer: c
MEDIUM
Which of the following statements is CORRECT?
a. A time line is not meaningful unless all cash flows occur annually.
b. Time lines are not useful for visualizing complex problems prior to
doing actual calculations.
c. Time lines can be constructed to deal with situations where some of
the cash flows occur annually but others occur quarterly.
d. Time lines can only be constructed for annuities where the payments
occur at the end of the periods, i.e., for ordinary annuities.
e. Time lines cannot be constructed where some of the payments
constitute an annuity but others are unequal and thus are not part of
the annuity.
(5-1) Time lines
38.
F J
Answer: e
MEDIUM
Which of the following statements is CORRECT?
a. A time line is not meaningful unless all cash flows occur annually.
b. Time lines are not useful for visualizing complex problems prior to
doing actual calculations.
c. Time lines cannot be constructed to deal with situations where some
of the cash flows occur annually but others occur quarterly.
d. Time lines can only be constructed for annuities where the payments
occur at the end of the periods, i.e., for ordinary annuities.
e. Time lines can be constructed where some of the payments constitute
an annuity but others are unequal and thus are not part of the
annuity.
(5-3) Effects of factors on PVs
39.
C J
Answer: b
MEDIUM
You plan to analyze the value of a potential investment by calculating
the sum of the present values of its expected cash flows. Which of the
following would lower the calculated value of the investment?
a. The cash flows are in the form of a deferred annuity, and they total
to $100,000. You learn that the annuity lasts for only 5 rather than
10 years, hence that each payment is for $20,000 rather than for
$10,000.
b. The discount rate increases.
c. The riskiness of the investment’s cash flows decreases.
d. The total amount of cash flows remains the same, but more of the cash
flows are received in the earlier years and less are received in the
later years.
e. The discount rate decreases.
(5-3) Effects of factors on PVs
40.
C J
Answer: b
MEDIUM
You plan to analyze the value of a potential investment by calculating
the sum of the present values of its expected cash flows. Which of the
following would increase the calculated value of the investment?
a. The cash flows are in the form of a deferred annuity, and they total to
$100,000. You learn that the annuity lasts for 10 years rather than 5
years, hence that each payment is for $10,000 rather than for $20,000.
b. The discount rate decreases.
c. The riskiness of the investment’s cash flows increases.
d. The total amount of cash flows remains the same, but more of the cash
flows are received in the later years and less are received in the
earlier years.
e. The discount rate increases.
Chapter 5: Time Value of Money
Conceptual M/C
Page 141
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-6) Annuities
41.
F J
Answer: d
MEDIUM
Which of the following statements is CORRECT?
a. The cash flows for an ordinary (or deferred) annuity all occur at the
beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, such
as once a year, then the series is by definition an annuity.
c. The cash flows for an annuity due must all occur at the ends of the
periods.
d. The cash flows for an annuity must all be equal, and they must occur
at regular intervals, such as once a year or once a month.
e. If some cash flows occur at the beginning of the periods while others
occur at the ends, then we have what the textbook defines as a
variable annuity.
(5-6) Annuities
42.
F J
Answer: c
MEDIUM
Which of the following statements is CORRECT?
a. The cash flows for an ordinary (or deferred) annuity all occur at the
beginning of the periods.
b. If a series of unequal cash flows occurs at regular intervals, such
as once a year, then the series is by definition an annuity.
c. The cash flows for an annuity due must all occur at the beginning of
the periods.
d. The cash flows for an annuity may vary from period to period, but
they must occur at regular intervals, such as once a year or once a
month.
e. If some cash flows occur at the beginning of the periods while others
occur at the ends, then we have what the textbook defines as a
variable annuity.
(5-16) Quarterly compounding
43.
C J
Answer: c
MEDIUM
Your bank account pays a 6% nominal rate of interest. The interest is
compounded quarterly. Which of the following statements is CORRECT?
a. The periodic rate of interest
interest is 3%.
b. The periodic rate of interest
interest is greater than 6%.
c. The periodic rate of interest
interest is greater than 6%.
d. The periodic rate of interest
interest is 6%.
e. The periodic rate of interest
interest is also 6%.
Page 142
is 1.5% and the effective rate of
is 6% and the effective rate of
is 1.5% and the effective rate of
is 3% and the effective rate of
is 6% and the effective rate of
Conceptual M/C
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-16) Quarterly compounding
44.
C J
MEDIUM
Your bank account pays an 8% nominal rate of interest. The interest is
compounded quarterly. Which of the following statements is CORRECT?
a. The periodic rate of interest
interest is 4%.
b. The periodic rate of interest
interest is greater than 8%.
c. The periodic rate of interest
interest is less than 8%.
d. The periodic rate of interest
interest is greater than 8%.
e. The periodic rate of interest
interest is also 8%.
(5-18) Amortization
45.
Answer: d
is 2% and the effective rate of
is 8% and the effective rate of
is 4% and the effective rate of
is 2% and the effective rate of
is 8% and the effective rate of
C J
Answer: c
MEDIUM
A $50,000 loan is to be amortized over 7 years, with annual end-of-year
payments. Which of these statements is CORRECT?
a. The annual payments would be larger if the interest rate were lower.
b. If the loan were amortized over 10 years rather than 7 years, and if
the interest rate were the same in either case, the first payment
would include more dollars of interest under the 7-year amortization
plan.
c. The proportion of each payment that represents interest as opposed to
repayment of principal would be lower if the interest rate were
lower.
d. The last payment would have a higher proportion of interest than the
first payment.
e. The proportion of interest versus principal repayment would be the
same for each of the 7 payments.
(5-18) Amortization
46.
C J
Answer: d
MEDIUM
A $150,000 loan is to be amortized over 7 years, with annual end-of-year
payments. Which of these statements is CORRECT?
a. The annual payments would be larger if the interest rate were lower.
b. If the loan were amortized over 10 years rather than 7 years, and if
the interest rate were the same in either case, the first payment
would include more dollars of interest under the 7-year amortization
plan.
c. The proportion of each payment that represents interest as opposed to
repayment of principal would be higher if the interest rate were
lower.
d. The proportion of each payment that represents interest versus
repayment of principal would be higher if the interest rate were
higher.
e. The proportion of interest versus principal repayment would be the
same for each of the 7 payments.
Chapter 5: Time Value of Money
Conceptual M/C
Page 143
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(5-18) Amortization
47.
C J
Answer: b
MEDIUM
Which of the following statements regarding a 15-year (180-month)
$125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and
transactions costs.)
a. The remaining balance after three years will be $125,000 less one
third of the interest paid during the first three years.
b. Because it is a fixed-rate mortgage, the monthly loan payments (which
include both interest and principal payments) are constant.
c. Interest payments on the mortgage will increase steadily over time,
but the total amount of each payment will remain constant.
d. The proportion of the monthly payment that goes towards repayment of
principal will be lower 10 years from now than it will be the first
year.
e. The outstanding balance declines at a slower rate in the later years
of the loan’s life.
(5-18) Amortization
48.
C J
Answer: e
MEDIUM
Which of the following statements regarding a 15-year (180-month)
$125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and
transactions costs.)
a. The remaining balance after three years will be $125,000 less one
third of the interest paid during the first three years.
b. Because the outstanding balance declines over time, the monthly
payments will also decline over time.
c. Interest payments on the mortgage will increase steadily over time,
but the total amount of each payment will remain constant.
d. The proportion of the monthly payment that goes towards repayment of
principal will be lower 10 years from now than it will be the first
year.
e. The outstanding balance declines at a faster rate in the later years
of the loan’s life.
(5-18) Amortization
49.
C J
Answer: b
MEDIUM
Which of the following statements regarding a 30-year monthly payment
amortized mortgage with a nominal interest rate of 10% is CORRECT?
a. The monthly payments will decline over time.
b. A smaller proportion of the last monthly payment will be interest,
and a larger proportion will be principal, than for the first monthly
payment.
c. The total dollar amount of principal being paid off each month gets
smaller as the loan approaches maturity.
d. The amount representing interest in the first payment would be higher
if the nominal interest rate were 7% rather than 10%.
e. Exactly 10% of the first monthly payment represents interest.
Page 144
Conceptual M/C
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-18) Amortization
50.
C J
Answer: b
MEDIUM
Which of the following statements regarding a 30-year monthly payment
amortized mortgage with a nominal interest rate of 10% is CORRECT?
a. The monthly payments will increase over time.
b. A larger proportion of the first monthly payment will be interest,
and a smaller proportion will be principal, than for the last monthly
payment.
c. The total dollar amount of interest being paid off each month gets
larger as the loan approaches maturity.
d. The amount representing interest in the first payment would be higher
if the nominal interest rate were 7% rather than 10%.
e. Exactly 10% of the first monthly payment represents interest.
(Comp.) Time value concepts
51.
C J
Answer: a
MEDIUM
Which of the following investments would have the highest future value
at the end of 10 years? Assume that the effective annual rate for all
investments is the same and is greater than zero.
a. Investment A pays $250 at the beginning of every year for the next 10
years (a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the
next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for
the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the end of every year for the next 10 years
(a total of 10 payments).
(Comp.) Time value concepts
52.
C J
Answer: d
MEDIUM
Which of the following investments would have the lowest present value?
Assume that the effective annual rate for all investments is the same
and is greater than zero.
a. Investment A pays $250 at the end of every year for the next 10 years
(a total of 10 payments).
b. Investment B pays $125 at the end of every 6-month period for the
next 10 years (a total of 20 payments).
c. Investment C pays $125 at the beginning of every 6-month period for
the next 10 years (a total of 20 payments).
d. Investment D pays $2,500 at the end of 10 years (just one payment).
e. Investment E pays $250 at the beginning of every year for the next 10
years (a total of 10 payments).
(Comp.) Time value concepts
53.
C J
Answer: d
MEDIUM
A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from
today. The nominal interest rate is 6%, semiannual compounding. Which
of the following statements is CORRECT?
a. The periodic interest rate is greater than 3%.
b. The periodic rate is less than 3%.
c. The present value would be greater if the lump sum were discounted
back for more periods.
d. The present value of the $1,000 would be smaller if interest were
compounded monthly rather than semiannually.
e. The PV of the $1,000 lump sum has a higher present value than the PV
of a 3-year, $333.33 ordinary annuity.
Chapter 5: Time Value of Money
Conceptual M/C
Page 145
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(Comp.) Time value concepts
54.
C J
Answer: e
MEDIUM
A U.S. Treasury bond will pay a lump sum of $1,000 exactly 3 years from
today. The nominal interest rate is 6%, semiannual compounding. Which
of the following statements is CORRECT?
a. The periodic interest rate is greater than 3%.
b. The periodic rate is less than 3%.
c. The present value would be greater if the lump sum were discounted
back for more periods.
d. The present value of the $1,000 would be larger if interest were
compounded monthly rather than semiannually.
e. The PV of the $1,000 lump sum has a smaller present value than the PV
of a 3-year, $333.33 ordinary annuity.
(Comp.) Time value concepts
55.
C J
Answer: c
MEDIUM
Which of the following statements is CORRECT, assuming positive interest
rates and holding other things constant?
a. The present value of a 5-year, $250 annuity due will be lower than
the PV of a similar ordinary annuity.
b. A 30-year, $150,000 amortized mortgage will have larger monthly
payments than an otherwise similar 20-year mortgage.
c. A bank loan's nominal interest rate will always be equal to or less
than its effective annual rate.
d. If an investment pays 10% interest, compounded annually, its
effective annual rate will be less than 10%.
e. Banks A and B offer the same nominal annual rate of interest, but A
pays interest quarterly and B pays semiannually. Deposits in Bank B
will provide the higher future value if you leave your funds on
deposit.
(Comp.) Time value concepts
56.
C J
Answer: d
MEDIUM
Which of the following statements is CORRECT, assuming positive interest
rates and holding other things constant?
a. The present value of a 5-year, $250 annuity due will be lower than
the PV of a similar ordinary annuity.
b. A 30-year, $150,000 amortized mortgage will have larger monthly
payments than an otherwise similar 20-year mortgage.
c. A bank loan's nominal interest rate will always be equal to or
greater than its effective annual rate.
d. If an investment pays 10% interest, compounded quarterly, its
effective annual rate will be greater than 10%.
e. Banks A and B offer the same nominal annual rate of interest, but A
pays interest quarterly and B pays semiannually. Deposits in Bank B
will provide the higher future value if you leave your funds on
deposit.
Page 146
Conceptual M/C
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(Comp.) Time value concepts
57.
C J
Answer: a
MEDIUM
Which of the following statements is CORRECT?
a. The present value of a 3-year, $150 annuity due will exceed the
present value of a 3-year, $150 ordinary annuity.
b. If a loan has a nominal annual rate of 8%, then the effective rate
can never be greater than 8%.
c. If a loan or investment has annual payments, then the effective,
periodic, and nominal rates of interest will all be different.
d. The proportion of the payment that goes toward interest on a fully
amortized loan increases over time.
e. An investment that has a nominal rate of 6% with semiannual payments
will have an effective rate that is smaller than 6%.
(Comp.) Time value concepts
58.
C J
Answer: b
MEDIUM
Which of the following statements is CORRECT?
a. The present value of a 3-year, $150 ordinary annuity will exceed the
present value of a 3-year, $150 annuity due.
b. If a loan has a nominal annual rate of 8%, then the effective rate
will never be less than 8%.
c. If a loan or investment has annual payments, then the effective,
periodic, and nominal rates of interest will all be different.
d. The proportion of the payment that goes toward interest on a fully
amortized loan increases over time.
e. An investment that has a nominal rate of 6% with semiannual payments
will have an effective rate that is smaller than 6%.
(Comp.) Annuities
59.
C J
Answer: d
MEDIUM
You are considering two equally risky annuities, each of which pays
$5,000 per year for 10 years. Investment ORD is an ordinary (or
deferred) annuity, while Investment DUE is an annuity due. Which of the
following statements is CORRECT?
a. The present value of ORD must exceed the present value of DUE, but
the future value of ORD may be less than the future value of DUE.
b. The present value of DUE exceeds the present value of ORD, while the
future value of DUE is less than the future value of ORD.
c. The present value of ORD exceeds the present value of DUE, and the
future value of ORD also exceeds the future value of DUE.
d. The present value of DUE exceeds the present value of ORD, and the
future value of DUE also exceeds the future value of ORD.
e. If the going rate of interest decreases from 10% to 0%, the
difference between the present value of ORD and the present value of
DUE would remain constant.
Chapter 5: Time Value of Money
Conceptual M/C
Page 147
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(Comp.) Annuities
60.
C J
Answer: a
MEDIUM
You are considering two equally risky annuities, each of which pays
$5,000 per year for 10 years. Investment ORD is an ordinary (or
deferred) annuity, while Investment DUE is an annuity due. Which of the
following statements is CORRECT?
a. A rational investor would be willing to pay more for DUE than for
ORD, so their market prices should differ.
b. The present value of DUE exceeds the present value of ORD, while the
future value of DUE is less than the future value of ORD.
c. The present value of ORD exceeds the present value of DUE, and the
future value of ORD also exceeds the future value of DUE.
d. The present value of ORD exceeds the present value of DUE, while the
future value of DUE exceeds the future value of ORD.
e. If the going rate of interest decreases from 10% to 0%, the
difference between the present value of ORD and the present value of
DUE would remain constant.
(5-14) Solving for I: uneven CFs
61.
C J
Answer: c
HARD
Which of the following statements is CORRECT?
a. If you have a series of cash flows, each of which is positive, you
can solve for I, where the solution value of I causes the PV of the
cash flows to equal the cash flow at Time 0.
b. If you have a series of cash flows, and CF0 is negative but each of
the following CFs is positive, you can solve for I, but only if the
sum of the undiscounted cash flows exceeds the cost.
c. To solve for I, one must identify the value of I that causes the PV
of the positive CFs to equal the absolute value of the PV of the
negative CFs. This is, essentially, a trial-and-error procedure that
is easy with a computer or financial calculator but quite difficult
otherwise.
d. If you solve for I and get a negative number, then you must have made
a mistake.
e. If CF0 is positive and all the other CFs are negative, then you
cannot solve for I.
(5-14) Solving for I: uneven CFs
62.
C J
Answer: e
HARD
Which of the following statements is CORRECT?
a. If you have a series of cash flows, each of which is positive, you
can solve for I, where the solution value of I causes the PV of the
cash flows to equal the cash flow at Time 0.
b. If you have a series of cash flows, and CF0 is negative but each of
the following CFs is positive, you can solve for I, but only if the
sum of the undiscounted cash flows exceeds the cost.
c. To solve for I, one must identify the value of I that causes the PV
of the positive CFs to equal the absolute value of the FV of the
negative CFs. It is impossible to find the value of I without a
computer or financial calculator.
d. If you solve for I and get a negative number, then you must have made
a mistake.
e. If CF0 is positive and all the other CFs are negative, then you can
still solve for I.
Page 148
Conceptual M/C
Chapter 5: Time Value of Money
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(5-16) Effective annual rate
63.
HARD
pays 8% nominal interest with monthly compounding.
pays 8% nominal interest with annual compounding.
pays 7% nominal interest with daily (365-day)
pays 7% nominal interest with monthly compounding.
pays 8% nominal interest with daily (365-day)
(5-16) Effective annual rate
C J
Answer: d
HARD
Which of the following bank accounts has the lowest effective annual
return?
a. An account that
b. An account that
c. An account that
compounding.
d. An account that
e. An account that
compounding.
pays 8% nominal interest with monthly compounding.
pays 8% nominal interest with annual compounding.
pays 7% nominal interest with daily (365-day)
pays 7% nominal interest with monthly compounding.
pays 8% nominal interest with daily (365-day)
(5-16) Effective annual rate
65.
Answer: e
Which of the following bank accounts has the highest effective annual
return?
a. An account that
b. An account that
c. An account that
compounding.
d. An account that
e. An account that
compounding.
64.
C J
C J
Answer: e
HARD
You plan to invest some money in a bank account. Which of the following
banks provides you with the highest effective rate of interest?
a.
b.
c.
d.
e.
Bank
Bank
Bank
Bank
Bank
1;
2;
3;
4;
5;
6.1%
6.0%
6.0%
6.0%
6.0%
with
with
with
with
with
annual compounding.
monthly compounding.
annual compounding.
quarterly compounding.
daily (365-day) compounding.
Multiple Choice: Problems
(5-2) FV of a lump sum
66.
Answer: d
EASY
Sue now has $125. How much would she have after 8 years if she leaves
it invested at 8.5% with annual compounding?
a.
b.
c.
d.
e.
$205.83
$216.67
$228.07
$240.08
$252.08
(5-2) FV of a lump sum
67.
C J
C J
Answer: d
EASY
Jose now has $500. How much would he have after 6 years if he leaves it
invested at 5.5% with annual compounding?
a.
b.
c.
d.
e.
$591.09
$622.20
$654.95
$689.42
$723.89
Chapter 5: Time Value of Money
M/C Problems
Page 149
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(5-2) FV of a lump sum
68.
Answer: a
EASY
$3,754.27
$3,941.99
$4,139.09
$4,346.04
$4,563.34
(5-2) FV of a lump sum
C J
Answer: c
EASY
Last year Rocco Corporation's sales were $225 million. If sales grow at
6% per year, how large (in millions) will they be 5 years later?
a.
b.
c.
d.
e.
$271.74
$286.05
$301.10
$316.16
$331.96
(5-2) FV of a lump sum
C J
Answer: c
EASY
Last year Dania Corporation's sales were $525 million. If sales grow at
7.5% per year, how large (in millions) will they be 8 years later?
a.
b.
c.
d.
e.
$ 845.03
$ 889.51
$ 936.33
$ 983.14
$1,032.30
(5-2) FV of a lump sum
72.
C J
Suppose you have $2,000 and plan to purchase a 10-year certificate of
deposit (CD) that pays 6.5% interest, compounded annually. How much
will you have when the CD matures?
a.
b.
c.
d.
e.
71.
EASY
$1,781.53
$1,870.61
$1,964.14
$2,062.34
$2,165.46
(5-2) FV of a lump sum
70.
Answer: a
Suppose you have $1,500 and plan to purchase a 5-year certificate of
deposit (CD) that pays 3.5% interest, compounded annually. How much
will you have when the CD matures?
a.
b.
c.
d.
e.
69.
C J
C J
Answer: b
EASY
How much would $1, growing at 3.5% per year, be worth after 75 years?
a.
b.
c.
d.
e.
Page 150
$12.54
$13.20
$13.86
$14.55
$15.28
M/C Problems
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-2) FV of a lump sum
73.
Answer: b
EASY
$2,245.08
$2,363.24
$2,481.41
$2,605.48
$2,735.75
(5-2) FV of a lump sum
C J
Answer: b
EASY
You deposit $500 today in a savings account that pays 3.5% interest,
compounded annually. How much will your account be worth at the end of
25 years?
a.
b.
c.
d.
e.
$1,122.54
$1,181.62
$1,240.70
$1,302.74
$1,367.88
(5-3) PV of a lump sum
C J
Answer: a
EASY
Suppose a State of New York bond will pay $1,000 ten years from now. If
the going interest rate on these 10-year bonds is 5.5%, how much is the
bond worth today?
a.
b.
c.
d.
e.
$585.43
$614.70
$645.44
$677.71
$711.59
(5-3) PV of a lump sum
77.
C J
You deposit $1,000 today in a savings account that pays 3.5% interest,
compounded annually. How much will your account be worth at the end of
25 years?
a.
b.
c.
d.
e.
76.
EASY
$3,689.11
$3,883.27
$4,077.43
$4,281.30
$4,495.37
(5-2) FV of a lump sum
75.
Answer: b
How much would $100, growing at 5% per year, be worth after 75 years?
a.
b.
c.
d.
e.
74.
C J
C J
Answer: a
EASY
Suppose a State of California bond will pay $1,000 eight years from now.
If the going interest rate on these 8-year bonds is 5.5%, how much is
the bond worth today?
a.
b.
c.
d.
e.
$651.60
$684.18
$718.39
$754.31
$792.02
Chapter 5: Time Value of Money
M/C Problems
Page 151
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(5-3) PV of a lump sum
78.
Answer: e
EASY
$1,067.95
$1,124.16
$1,183.33
$1,245.61
$1,311.17
(5-3) PV of a lump sum
C J
Answer: b
EASY
Suppose a U.S. treasury bond will pay $2,500 five years from now. If
the going interest rate on 5-year treasury bonds is 4.25%, how much is
the bond worth today?
a.
b.
c.
d.
e.
$1,928.78
$2,030.30
$2,131.81
$2,238.40
$2,350.32
(5-3) PV of a lump sum
C J
Answer: b
EASY
Suppose an Exxon Corporation bond will pay $4,500 ten years from now.
If the going interest rate on safe 10-year bonds is 4.25%, how much is
the bond worth today?
a.
b.
c.
d.
e.
$2,819.52
$2,967.92
$3,116.31
$3,272.13
$3,435.74
(5-4) Finding I
82.
C J
How much would $5,000 due in 25 years be worth today if the discount
rate were 5.5%?
a.
b.
c.
d.
e.
81.
EASY
$438.03
$461.08
$485.35
$510.89
$537.78
(5-3) PV of a lump sum
80.
Answer: e
How much would $20,000 due in 50 years be worth today if the discount
rate were 7.5%?
a.
b.
c.
d.
e.
79.
C J
C J
Answer: d
EASY
Suppose the U.S. Treasury offers to sell you a bond for $747.25. No
payments will be made until the bond matures 5 years from now, at which
time it will be redeemed for $1,000. What interest rate would you earn
if you bought this bond at the offer price?
a.
b.
c.
d.
e.
Page 152
4.37%
4.86%
5.40%
6.00%
6.60%
M/C Problems
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-4) Finding I
83.
Answer: b
EASY
15.17%
15.97%
16.77%
17.61%
18.49%
(5-4) Growth rate
C J
Answer: b
EASY
Five years ago, Weed Go Inc. earned $1.50 per share. Its earnings this
year were $3.20. What was the growth rate in earnings per share (EPS)
over the 5-year period?
a.
b.
c.
d.
e.
15.54%
16.36%
17.18%
18.04%
18.94%
(5-5) Finding N
C J
Answer: e
Janice has $5,000 invested in a bank that pays 3.8% annually.
will it take for her funds to triple?
a.
b.
c.
d.
e.
C J
Bob has $2,500 invested in a bank that pays 4% annually.
it take for his funds to double?
a.
b.
c.
d.
e.
EASY
How long
23.99
25.26
26.58
27.98
29.46
(5-5) Finding N
87.
C J
Ten years ago, Lucas Inc. earned $0.50 per share. Its earnings this
year were $2.20. What was the growth rate in earnings per share (EPS)
over the 10-year period?
a.
b.
c.
d.
e.
86.
EASY
3.82%
4.25%
4.72%
5.24%
5.77%
(5-4) Growth rate
85.
Answer: d
Suppose the U.S. Treasury offers to sell you a bond for $3,000. No
payments will be made until the bond matures 10 years from now, at which
time it will be redeemed for $5,000. What interest rate would you earn
if you bought this bond at the offer price?
a.
b.
c.
d.
e.
84.
C J
Answer: e
EASY
How long will
14.39
15.15
15.95
16.79
17.67
Chapter 5: Time Value of Money
M/C Problems
Page 153
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(5-5) Finding N
88.
Answer: e
EASY
5.14
5.71
6.35
7.05
7.84
(5-5) Finding N
C J
Answer: e
EASY
You plan to invest in bonds that pay 6.0%, compounded annually. If you
invest $10,000 today, how many years will it take for your investment to
grow to $30,000?
a.
b.
c.
d.
e.
12.37
13.74
15.27
16.97
18.85
(5-7) FV of ordinary annuity
C J
Answer: c
EASY
You want to buy a new sports car 3 years from now, and you plan to save
$4,200 per year, beginning one year from today. You will deposit your
savings in an account that pays 5.2% interest. How much will you have
just after you make the 3rd deposit, 3 years from now?
a.
b.
c.
d.
e.
$11,973
$12,603
$13,267
$13,930
$14,626
(5-7) FV of ordinary annuity
92.
C J
You plan to invest in securities that pay 8.0%, compounded annually. If
you invest $5,000 today, how many years will it take for your investment
to grow to $9,140.20?
a.
b.
c.
d.
e.
91.
EASY
9.29
10.33
11.47
12.75
14.02
(5-5) Finding N
90.
Answer: d
Last year Thomson Inc's earnings per share were $3.50, and its growth
rate during the prior 5 years was 9.0% per year. If that growth rate
were maintained, how many years would it take for Thomson’s EPS to
triple?
a.
b.
c.
d.
e.
89.
C J
C J
Answer: c
EASY
You want to buy a new ski boat 2 years from now, and you plan to save
$8,200 per year, beginning one year from today. You will deposit your
savings in an account that pays 6.2% interest. How much will you have
just after you make the 2nd deposit, 2 years from now?
a.
b.
c.
d.
e.
Page 154
$15,260
$16,063
$16,908
$17,754
$18,642
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-7) FV of ordinary annuity
93.
Answer: a
EASY
$16,112
$16,918
$17,763
$18,652
$19,584
(5-8) FV of annuity due
C J
Answer: c
EASY
You want to quit your job and return to school for an MBA degree 3 years
from now, and you plan to save $7,000 per year, beginning immediately.
You will make 3 deposits in an account that pays 5.2% interest. Under
these assumptions, how much will you have 3 years from today?
a.
b.
c.
d.
e.
$20,993
$22,098
$23,261
$24,424
$25,645
(5-9) PV of ordinary annuity
C J
Answer: e
EASY
What is the PV of an ordinary annuity with 10 payments of $2,700 if the
appropriate interest rate is 5.5%?
a.
b.
c.
d.
e.
$16,576
$17,449
$18,367
$19,334
$20,352
(5-9) PV of ordinary annuity
97.
C J
You want to quit your job and go back to school for a law degree 4 years
from now, and you plan to save $3,500 per year, beginning immediately.
You will make 4 deposits in an account that pays 5.7% interest. Under
these assumptions, how much will you have 4 years from today?
a.
b.
c.
d.
e.
96.
EASY
$18,369
$19,287
$20,251
$21,264
$22,327
(5-8) FV of annuity due
95.
Answer: a
You want to go to Europe 5 years from now, and you can save $3,100 per
year, beginning one year from today. You plan to deposit the funds in a
mutual fund that you think will return 8.5% per year. Under these
conditions, how much would you have just after you make the 5th deposit,
5 years from now?
a.
b.
c.
d.
e.
94.
C J
C J
Answer: e
EASY
What is the PV of an ordinary annuity with 5 payments of $4,700 if the
appropriate interest rate is 4.5%?
a.
b.
c.
d.
e.
$16,806
$17,690
$18,621
$19,601
$20,633
Chapter 5: Time Value of Money
M/C Problems
Page 155
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-9) PV of ordinary annuity
98.
Answer: e
EASY
$50,753
$53,424
$56,236
$59,195
$62,311
(5-9) PV of ordinary annuity
C J
Answer: b
EASY
Your aunt is about to retire, and she wants to sell some of her stock
and buy an annuity that will provide her with income of $50,000 per year
for 30 years, beginning a year from today. The going rate on such
annuities is 7.25%. How much would it cost her to buy such an annuity
today?
a.
b.
c.
d.
e.
$574,924
$605,183
$635,442
$667,214
$700,575
(5-9) PV of annuity due
C J
Answer: a
EASY
What is the PV of an annuity due with 5 payments of $2,500 at an
interest rate of 5.5%?
a.
b.
c.
d.
e.
$11,262.88
$11,826.02
$12,417.32
$13,038.19
$13,690.10
(5-11) PV of a perpetuity
102.
C J
You just inherited some money, and a broker offers to sell you an
annuity that pays $5,000 at the end of each year for 20 years. You
could earn 5% on your money in other investments with equal risk. What
is the most you should pay for the annuity?
a.
b.
c.
d.
e.
101.
EASY
$5,493.71
$5,782.85
$6,087.21
$6,407.59
$6,744.83
(5-9) PV of ordinary annuity
100.
Answer: e
You have a chance to buy an annuity that pays $2,500 at the end of each
year for 3 years. You could earn 5.5% on your money in other
investments with equal risk. What is the most you should pay for the
annuity?
a.
b.
c.
d.
e.
99.
C J
C J
Answer: b
EASY
What’s the present value of a perpetuity that pays $250 per year if the
appropriate interest rate is 5%?
a.
b.
c.
d.
e.
Page 156
$4,750
$5,000
$5,250
$5,513
$5,788
M/C Problems
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-11) Return on a perpetuity
103.
C J
Answer: a
EASY
What’s the rate of return you would earn if you paid $950 for a
perpetuity that pays $85 per year?
a. 8.95%
b. 9.39%
c. 9.86%
d. 10.36%
e. 10.88%
(5-9) PV of annuity due
104.
C J
Answer: c
MEDIUM
You have a chance to buy an annuity that pays $5,000 at the beginning of
each year for 5 years. You could earn 4.5% on your money in other
investments with equal risk. What is the most you should pay for the
annuity?
a.
b.
c.
d.
e.
$20,701
$21,791
$22,938
$24,085
$25,289
(5-9) PV of annuity due
C J
Answer: d
MEDIUM
Your uncle is about to retire, and he wants to buy an annuity that will
provide him with $75,000 of income a year for 20 years, with the first
payment coming immediately. The going rate on such annuities is 5.25%.
How much would it cost him to buy the annuity today?
a.
b.
c.
d.
e.
$ 825,835
$ 869,300
$ 915,052
$ 963,213
$1,011,374
(5-9) PV of annuity due
107.
MEDIUM
$1,412.84
$1,487.20
$1,565.48
$1,643.75
$1,725.94
(5-9) PV of annuity due
106.
Answer: c
You have a chance to buy an annuity that pays $550 at the beginning of
each year for 3 years. You could earn 5.5% on your money in other
investments with equal risk. What is the most you should pay for the
annuity?
a.
b.
c.
d.
e.
105.
C J
C J
Answer: d
MEDIUM
Your father is about to retire, and he wants to buy an annuity that will
provide him with $85,000 of income a year for 25 years, with the first
payment coming immediately. The going rate on such annuities is 5.15%.
How much would it cost him to buy the annuity today?
a.
b.
c.
d.
e.
$1,063,968
$1,119,966
$1,178,912
$1,240,960
$1,303,008
Chapter 5: Time Value of Money
M/C Problems
Page 157
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(5-9) PV of annuity due
108.
Answer: b
MEDIUM
$225,367
$237,229
$249,090
$261,545
$274,622
(5-9) PV of ord. ann. & end. pmt.
C J
Answer: e
MEDIUM
What’s the present value of a 4-year ordinary annuity of $2,250 per year
plus an additional $3,000 at the end of Year 4 if the interest rate is
5%?
a.
b.
c.
d.
e.
$ 8,509
$ 8,957
$ 9,428
$ 9,924
$10,446
(5-10) Ord. annuity payments
C J
Answer: a
Suppose you inherited $275,000 and invested it at 8.25% per year.
much could you withdraw at the end of each of the next 20 years?
a.
b.
c.
d.
e.
MEDIUM
How
$28,532
$29,959
$31,457
$33,030
$34,681
(5-10) Ord. annuity payments
112.
C J
Sam was injured in an accident, and the insurance company has offered
him the choice of $25,000 per year for 15 years, with the first payment
being made today, or a lump sum. If a fair return is 7.5%, how large
must the lump sum be to leave him as well off financially as with the
annuity?
a.
b.
c.
d.
e.
111.
MEDIUM
$284,595
$299,574
$314,553
$330,281
$346,795
(5-9) PV of annuity due
110.
Answer: b
You inherited an oil well that will pay you $25,000 per year for 25
years, with the first payment being made today. If you think a fair
return on the well is 7.5%, how much should you ask for it if you decide
to sell it?
a.
b.
c.
d.
e.
109.
C J
C J
Answer: d
MEDIUM
Your uncle has $375,000 and wants to retire. He expects to live for
another 25 years and to earn 7.5% on his invested funds. How much could
he withdraw at the end of each of the next 25 years and end up with zero
in the account?
a.
b.
c.
d.
e.
Page 158
$28,843.38
$30,361.46
$31,959.43
$33,641.50
$35,323.58
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-10) Annuity due payments
113.
C J
Answer: c
MEDIUM
Your grandmother just died and left you $100,000 in a trust fund that
pays 6.5% interest. You must spend the money on your college education,
and you must withdraw the money in 4 equal installments, beginning
immediately. How much could you withdraw today and at the beginning of
each of the next 3 years and end up with zero in the account?
a.
b.
c.
d.
e.
$24,736
$26,038
$27,409
$28,779
$30,218
(5-10) Annuity due payments
C J
Answer: d
MEDIUM
Suppose you inherited $275,000 and invested it at 8.25% per year. How
much could you withdraw at the beginning of each of the next 20 years?
a.
b.
c.
d.
e.
$22,598.63
$23,788.03
$25,040.03
$26,357.92
$27,675.82
(5-10) Finding annuity periods
116.
MEDIUM
$28,243.21
$29,729.70
$31,294.42
$32,859.14
$34,502.10
(5-10) Annuity due payments
115.
Answer: c
Your uncle has $375,000 and wants to retire. He expects to live for
another 25 years, and he also expects to earn 7.5% on his invested
funds. How much could he withdraw at the beginning of each of the next
25 years and end up with zero in the account?
a.
b.
c.
d.
e.
114.
C J
C J
Answer: a
MEDIUM
Your father's employer was just acquired, and he was given a severance
payment of $375,000, which he invested at a 7.5% annual rate. He now
plans to retire, and he wants to withdraw $35,000 at the end of each
year, starting at the end of this year. How many years will it take to
exhaust his funds, i.e., run the account down to zero?
a.
b.
c.
d.
e.
22.50
23.63
24.81
26.05
27.35
Chapter 5: Time Value of Money
M/C Problems
Page 159
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(5-10) Finding annuity periods
117.
C J
14.21
14.96
15.71
16.49
17.32
(5-10) Finding annuity due periods
Answer: e
MEDIUM
18.62
19.60
20.63
21.71
22.86
(5-10) Finding annuity due periods
C J
Answer: c
MEDIUM
Your aunt has $500,000 invested at 5.5%, and she now wants to retire.
She wants to withdraw $45,000 at the beginning of each year, beginning
immediately. She also wants to have $50,000 left to give you when she
ceases to withdraw funds from the account. For how many years can she
make the $45,000 withdrawals and still have $50,000 left in the end?
a.
b.
c.
d.
e.
15.54
16.36
17.22
18.08
18.99
(5-10) Finding I: annuity
120.
C J
Your Aunt Ruth has $500,000 invested at 6.5%, and she plans to retire.
She wants to withdraw $40,000 at the beginning of each year, starting
immediately. How many years will it take to exhaust her funds, i.e.,
run the account down to zero?
a.
b.
c.
d.
e.
119.
MEDIUM
Your uncle has $300,000 invested at 7.5%, and he now wants to retire.
He wants to withdraw $35,000 at the end of each year, starting at the
end of this year. He also wants to have $25,000 left to give you when
he ceases to withdraw funds from the account. For how many years can he
make the $35,000 withdrawals and still have $25,000 left in the end?
a.
b.
c.
d.
e.
118.
Answer: b
C J
Answer: b
MEDIUM
Suppose you just won the state lottery, and you have a choice between
receiving $2,550,000 today or a 20-year annuity of $250,000, with the
first payment coming one year from today. What rate of return is built
into the annuity? Disregard taxes.
a.
b.
c.
d.
e.
Page 160
7.12%
7.49%
7.87%
8.26%
8.67%
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-10) Finding I: annuity
121.
C J
3.44%
3.79%
4.17%
4.58%
5.04%
(5-10) Finding I: annuity due
C J
MEDIUM
6.85%
7.21%
7.59%
7.99%
8.41%
(5-11) Payments on a perpetuity
C J
Answer: b
MEDIUM
What annual payment must you receive in order to earn a 6.5% rate of
return on a perpetuity that has a cost of $1,250?
a.
b.
c.
d.
e.
$77.19
$81.25
$85.31
$89.58
$94.06
(5-12) PV of uneven cash flows
124.
Answer: e
Assume that you own an annuity that will pay you $15,000 per year for 12
years, with the first payment being made today. You need money today to
start a new business, and your uncle offers to give you $120,000 for the
annuity. If you sell it, what rate of return would your uncle earn on
his investment?
a.
b.
c.
d.
e.
123.
MEDIUM
Your girlfriend just won the Florida lottery. She has the choice of
$15,000,000 today or a 20-year annuity of $1,050,000, with the first
payment coming one year from today. What rate of return is built into
the annuity?
a.
b.
c.
d.
e.
122.
Answer: a
C J
Answer: e
MEDIUM
What is the present value of the following cash flow stream at a rate of
6.25%?
Years:
CFs:
a.
b.
c.
d.
e.
0
|
$0
1
|
$75
2
|
$225
3
|
$0
4
|
$300
$411.57
$433.23
$456.03
$480.03
$505.30
Chapter 5: Time Value of Money
M/C Problems
Page 161
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(5-12) PV of uneven cash flows
125.
C J
CFs:
a.
b.
c.
d.
e.
0
|
$0
1
|
$1,500
3
|
$4,500
4
|
$6,000
C J
Answer: d
MEDIUM
What is the present value of the following cash flow stream at a rate of
8.0%?
Years:
CFs:
a.
b.
c.
d.
e.
0
|
$750
1
|
$2,450
2
|
$3,175
3
|
$4,400
$7,917
$8,333
$8,772
$9,233
$9,695
(5-12) PV of uneven cash flows
C J
Answer: a
MEDIUM
You sold a car and accepted a note with the following cash flow stream
as your payment. What was the effective price you received for the car
assuming an interest rate of 6.0%?
Years:
CFs:
a.
b.
c.
d.
e.
0
|
$0
1
|
$1,000
2
|
$2,000
3
|
$2,000
4
|
$2,000
$5,987
$6,286
$6,600
$6,930
$7,277
(5-13) FV of uneven cash flows
128.
2
|
$3,000
$ 9,699
$10,210
$10,747
$11,284
$11,849
(5-12) PV of uneven cash flows
127.
MEDIUM
What is the present value of the following cash flow stream at a rate of
12.0%?
Years:
126.
Answer: c
C J
Answer: e
MEDIUM
At a rate of 6.5%, what is the future value of the following cash flow
stream?
Years:
CFs:
a.
b.
c.
d.
e.
Page 162
0
|
$0
1
|
$75
2
|
$225
3
|
$0
4
|
$300
$526.01
$553.69
$582.83
$613.51
$645.80
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-14) Rate in uneven cash flows
129.
Answer: e
MEDIUM
4.93%
5.19%
5.46%
5.75%
6.05%
(5-15) FV, semiannual compounding
C J
Answer: c
MEDIUM
What’s the future value of $1,500 after 5 years if the appropriate
interest rate is 6%, compounded semiannually?
a.
b.
c.
d.
e.
$1,819
$1,915
$2,016
$2,117
$2,223
(5-15) FV, semiannual compounding
C J
Answer: d
MEDIUM
What’s the present value of $4,500 discounted back 5 years if the
appropriate interest rate is 4.5%, compounded semiannually?
a.
b.
c.
d.
e.
$3,089
$3,251
$3,422
$3,602
$3,782
(5-15) FV, monthly compounding
133.
C J
You are offered a chance to buy an asset for $7,250 that is expected to
produce cash flows of $750 at the end of Year 1, $1,000 at the end of
Year 2, $850 at the end of Year 3, and $6,250 at the end of Year 4.
What rate of return would you earn if you bought this asset?
a.
b.
c.
d.
e.
132.
MEDIUM
6.77%
7.13%
7.50%
7.88%
8.27%
(5-14) Rate in uneven cash flows
131.
Answer: c
Your father paid $10,000 (CF at t = 0) for an investment that promises
to pay $750 at the end of each of the next 5 years, then an additional
lump sum payment of $10,000 at the end of the 5th year. What is the
expected rate of return on this investment?
a.
b.
c.
d.
e.
130.
C J
C J
Answer: b
MEDIUM
What’s the future value of $1,200 after 5 years if the appropriate
interest rate is 6%, compounded monthly?
a.
b.
c.
d.
e.
$1,537.69
$1,618.62
$1,699.55
$1,784.53
$1,873.76
Chapter 5: Time Value of Money
M/C Problems
Page 163
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-15) PV, monthly compounding
134.
Answer: b
MEDIUM
18.58%
19.56%
20.54%
21.57%
22.65%
(5-16) Comparing EFF%
C J
Answer: d
MEDIUM
Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%,
compounded monthly. The loan (principal plus interest) must be repaid
at the end of the year. Midwest Bank also offers to lend you the
$50,000, but it will charge an annual rate of 7.0%, with no interest due
until the end of the year. How much higher or lower is the effective
annual rate charged by Midwest versus the rate charged by Riverside?
a.
b.
c.
d.
e.
0.52%
0.44%
0.36%
0.30%
0.24%
(5-16) Nominal rate vs. EFF%
C J
Answer: a
MEDIUM
Suppose Community Bank offers to lend you $10,000 for one year at a
nominal annual rate of 8.00%, but you must make interest payments at the
end of each quarter and then pay off the $10,000 principal amount at the
end of the year. What is the effective annual rate on the loan?
a.
b.
c.
d.
e.
8.24%
8.45%
8.66%
8.88%
9.10%
(5-16) Nominal rate vs. EFF%
138.
C J
Master Card and other credit card issuers must by law print the Annual
Percentage Rate (APR) on their monthly statements. If the APR is stated
to be 18.00%, with interest paid monthly, what is the card's EFF%?
a.
b.
c.
d.
e.
137.
MEDIUM
$ 969
$1,020
$1,074
$1,131
$1,187
(5-16) APR vs. EFF%
136.
Answer: d
What’s the present value of $1,525 discounted back 5 years if the
appropriate interest rate is 6%, compounded monthly?
a.
b.
c.
d.
e.
135.
C J
C J
Answer: e
MEDIUM
Suppose a bank offers to lend you $10,000 for 1 year on a loan contract
that calls for you to make interest payments of $250.00 at the end of
each quarter and then pay off the principal amount at the end of the
year. What is the effective annual rate on the loan?
a. 8.46%
b. 8.90%
c. 9.37%
d. 9.86%
e. 10.38%
Page 164
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-16) Nominal rate vs. EFF%
139.
Answer: b
MEDIUM
15.27%
16.08%
16.88%
17.72%
18.61%
(5-17) Simple interest
C J
Answer: a
MEDIUM
Pace Co. borrowed $20,000 at a rate of 7.25%, simple interest, with
interest paid at the end of each month. The bank uses a 360-day year.
How much interest would Pace have to pay in a 30-day month?
a.
b.
c.
d.
e.
$120.83
$126.88
$133.22
$139.88
$146.87
(5-17) Fractional time periods
C J
Answer: a
MEDIUM
Suppose you deposited $5,000 in a bank account that pays 5.25% with
daily compounding based on a 360-day year. How much would be in the
account after 8 months, assuming each month has 30 days?
a.
b.
c.
d.
e.
$5,178.09
$5,436.99
$5,708.84
$5,994.28
$6,294.00
(5-18) Amortization: payment
143.
C J
Suppose your credit card issuer states that it charges a 15.00% nominal
annual rate, but you must make monthly payments, which amounts to
monthly compounding. What is the effective annual rate?
a.
b.
c.
d.
e.
142.
MEDIUM
3.72%
4.13%
4.59%
5.05%
5.56%
(5-16) Nominal rate vs. EFF%
141.
Answer: c
Charter Bank pays a 4.50% nominal rate on deposits, with monthly
compounding. What effective annual rate (EFF%) does the bank pay?
a.
b.
c.
d.
e.
140.
C J
C J
Answer: a
MEDIUM
Suppose you borrowed $12,000 at a rate of 9.0% and must repay it in 4
equal installments at the end of each of the next 4 years. How large
would your payments be?
a.
b.
c.
d.
e.
$3,704.02
$3,889.23
$4,083.69
$4,287.87
$4,502.26
Chapter 5: Time Value of Money
M/C Problems
Page 165
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-18) Amortization: payment
144.
C J
Answer: e
MEDIUM
Your uncle will sell you his bicycle shop for $250,000, with “seller
financing,” at a 6.0% nominal annual rate. The terms of the loan would
require you to make 12 equal end-of-month payments per year for 4 years,
and then make an additional final (balloon) payment of $50,000 at the
end of the last month. What would your equal monthly payments be?
a.
b.
c.
d.
e.
$4,029.37
$4,241.44
$4,464.67
$4,699.66
$4,947.01
(5-18) Amortization: interest
C J
Answer: d
MEDIUM
Suppose you borrowed $14,000 at a rate of 10.0% and must repay it in 5
equal installments at the end of each of the next 5 years. How much
interest would you have to pay in the first year?
a.
b.
c.
d.
e.
$1,200.33
$1,263.50
$1,330.00
$1,400.00
$1,470.00
(5-18) Amortization: interest
147.
MEDIUM
$741.57
$780.60
$821.69
$862.77
$905.91
(5-18) Amortization: payment
146.
Answer: c
Suppose you are buying your first condo for $145,000, and you will make
a $15,000 down payment. You have arranged to finance the remainder with
a 30-year, monthly payment, amortized mortgage at a 6.5% nominal
interest rate, with the first payment due in one month. What will your
monthly payments be?
a.
b.
c.
d.
e.
145.
C J
C J
Answer: d
MEDIUM
You plan to borrow $35,000 at a 7.5% annual interest rate. The terms
require you to amortize the loan with 7 equal end-of-year payments. How
much interest would you be paying in Year 2?
a.
b.
c.
d.
e.
Page 166
$1,994.49
$2,099.46
$2,209.96
$2,326.27
$2,442.59
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-18) Amortization: interest
148.
C J
$7,531
$7,927
$8,323
$8,740
$9,177
(Comp.) N, ann. due, monthly comp.
Answer: d
MEDIUM
23
27
32
38
44
(Comp.) N, ann. due, monthly comp.
C J
Answer: b
MEDIUM
You are considering investing in a bank account that pays a nominal
annual rate of 7%, compounded monthly. If you invest $3,000 at the end
of each month, how many months will it take for your account to grow to
$150,000?
a.
b.
c.
d.
e.
39.60
44.00
48.40
53.24
58.57
(Comp.) Rate, ord. ann., monthly comp.
151.
C J
You are considering an investment in a Third World bank account that
pays a nominal annual rate of 18%, compounded monthly. If you invest
$5,000 at the beginning of each month, how many months would it take for
your account to grow to $250,000? Round fractional months up.
a.
b.
c.
d.
e.
150.
MEDIUM
Your bank offers to lend you $100,000 at an 8.5% annual interest rate to
start your new business. The terms require you to amortize the loan
with 10 equal end-of-year payments. How much interest would you be
paying in Year 2?
a.
b.
c.
d.
e.
149.
Answer: b
C J
Answer: d
MEDIUM
Your child’s orthodontist offers you two alternative payment plans. The
first plan requires a $4,000 immediate up-front payment. The second
plan requires you to make monthly payments of $137.41, payable at the
end of each month for 3 years. What nominal annual interest rate is
built into the monthly payment plan?
a.
b.
c.
d.
e.
12.31%
12.96%
13.64%
14.36%
15.08%
Chapter 5: Time Value of Money
M/C Problems
Page 167
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-10) N, lifetime vs. yearly
152.
C J
Answer: e
MEDIUM/HARD
Your subscription to Investing Wisely Weekly is about to expire. You
plan to subscribe to the magazine for the rest of your life, and you can
renew it by paying $85 annually, beginning immediately, or you can get a
lifetime subscription for $850, also payable immediately. Assuming that
you can earn 6.0% on your funds and that the annual renewal rate will
remain constant, how many years must you live to make the lifetime
subscription the better buy?
a. 7.48
b. 8.80
c. 10.35
d. 12.18
e. 14.33
(5-15) Non-annual compounding
153.
C J
$15,234.08
$16,035.87
$16,837.67
$17,679.55
$18,563.53
(5-16) Comparing EFF%
C J
Answer: d
MEDIUM/HARD
Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%,
simple interest, with interest paid quarterly. Merchants Bank offers to
lend you the $50,000, but it will charge 6.0%, simple interest, with
interest paid at the end of the year. What's the difference in the
effective annual rates charged by the two banks?
a.
b.
c.
d.
e.
1.56%
1.30%
1.09%
0.91%
0.72%
(5-18) Amortization: princ. repymt.
155.
MEDIUM/HARD
You just deposited $2,500 in a bank account that pays a 4.0% nominal
interest rate, compounded quarterly. If you also add another $5,000 to
the account one year (4 quarters) from now and another $7,500 to the
account two years (8 quarters) from now, how much will be in the account
three years (12 quarters) from now?
a.
b.
c.
d.
e.
154.
Answer: b
C J
Answer: b
MEDIUM/HARD
Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5
equal installments at the end of each of the next 5 years. By how much
would you reduce the amount you owe in the first year?
a.
b.
c.
d.
e.
Page 168
$2,404.91
$2,531.49
$2,658.06
$2,790.96
$2,930.51
M/C Problems
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-18) Amortization: ending bal.
156.
C J
Answer: c
MEDIUM/HARD
Your sister turned 35 today, and she is planning to save $7,000 per year
for retirement, with the first deposit to be made one year from today.
She will invest in a mutual fund that's expected to provide a return of
7.5% per year. She plans to retire 30 years from today, when she turns
65, and she expects to live for 25 years after retirement, to age 90.
Under these assumptions, how much can she spend each year after she
retires? Her first withdrawal will be made at the end of her first
retirement year.
a.
b.
c.
d.
e.
$58,601
$61,686
$64,932
$68,179
$71,588
(5-10) Finding I: annuity due
C J
Answer: a
HARD
You agree to make 24 deposits of $500 at the beginning of each month
into a bank account. At the end of the 24th month, you will have
$13,000 in your account. If the bank compounds interest monthly, what
nominal annual interest rate will you be earning?
a.
b.
c.
d.
e.
7.62%
8.00%
8.40%
8.82%
9.26%
(5-18) Amortization
159.
MEDIUM/HARD
$10,155.68
$10,690.19
$11,252.83
$11,845.09
$12,468.51
(Comp.) Retirement planning
158.
Answer: e
Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5
equal installments at the end of each of the next 5 years. How much
would you still owe at the end of the first year, after you have made
the first payment?
a.
b.
c.
d.
e.
157.
C J
C J
Answer: e
HARD
Your company has just taken out a 1-year installment loan for $72,500 at
a nominal rate of 11.0% but with equal end-of-month payments. What
percentage of the 2nd monthly payment will go toward the repayment of
principal?
a.
b.
c.
d.
e.
73.67%
77.55%
81.63%
85.93%
90.45%
Chapter 5: Time Value of Money
M/C Problems
Page 169
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(5-18) Amortization: interest
160.
C J
$17,419.55
$17,593.75
$17,769.68
$17,947.38
$18,126.85
(Comp.) Retirement planning
C J
Answer: a
HARD
Steve and Ed are cousins who were both born on the same day, and both
turned 25 today. Their grandfather began putting $2,500 per year into a
trust fund for Steve on his 20th birthday, and he just made a 6th
payment into the fund. The grandfather (or his estate's trustee) will
make 40 more $2,500 payments until a 46th and final payment is made on
Steve's 65th birthday. The grandfather set things up this way because
he wants Steve to work, not be a “trust fund baby,” but he also wants to
ensure that Steve is provided for in his old age.
Until now, the grandfather has been disappointed with Ed, hence
has not given him anything. However, they recently reconciled, and the
grandfather decided to make an equivalent provision for Ed. He will
make the first payment to a trust for Ed today, and he has instructed
his trustee to make 40 additional equal annual payments until Ed turns
65, when the 41st and final payment will be made. If both trusts earn
an annual return of 8%, how much must the grandfather put into Ed's
trust today and each subsequent year to enable him to have the same
retirement nest egg as Steve after the last payment is made on their
65th birthday?
a.
b.
c.
d.
e.
$3,726
$3,912
$4,107
$4,313
$4,528
(Comp.) FV comb. CF lump sum & ann.
162.
HARD
On January 1, 2010, your brother's business obtained a 30-year amortized
mortgage loan for $250,000 at a nominal annual rate of 7.0%, with 360
end-of-month payments. The firm can deduct the interest paid for tax
purposes. What will the interest tax deduction be for 2010?
a.
b.
c.
d.
e.
161.
Answer: a
C J
Answer: d
HARD
After graduation, you plan to work for Dynamo Corporation for 12 years
and then start your own business. You expect to save and deposit $7,500
a year for the first 6 years (t = 1 through t = 6) and $15,000 annually
for the following 6 years (t = 7 through t = 12). The first deposit
will be made a year from today. In addition, your grandfather just gave
you a $25,000 graduation gift which you will deposit immediately (t =
0). If the account earns 9% compounded annually, how much will you have
when you start your business 12 years from now?
a.
b.
c.
d.
e.
Page 170
$238,176
$250,712
$263,907
$277,797
$291,687
M/C Problems
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
(Comp.) CF for given return
163.
Answer: c
HARD
You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To
repay you, Breck will pay $2,500 at the end of Year 1, $5,000 at the end
of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently
unspecified cash flow, X, at the end of each year from Year 4 through
Year 7. Breck is essentially riskless, so you are confident the
payments will be made. You regard 8% as an appropriate rate of return
on a low risk but illiquid 7-year loan. What cash flow must the
investment provide at the end of each of the final 4 years, that is,
what is X?
a.
b.
c.
d.
e.
$4,271.67
$4,496.49
$4,733.15
$4,969.81
$5,218.30
(Comp.) Saving for college
164.
C J
C J
Answer: e
HARD
John and Daphne are saving for their daughter Ellen's college education.
Ellen just turned 10 (at t = 0), and she will be entering college 8
years from now (at t = 8). College tuition and expenses at State U. are
currently $14,500 a year, but they are expected to increase at a rate of
3.5% a year. Ellen should graduate in 4 years--if she takes longer or
wants to go to graduate school, she will be on her own. Tuition and
other costs will be due at the beginning of each school year (at t = 8,
9, 10, and 11).
So far, John and Daphne have accumulated $15,000 in their college
savings account (at t = 0). Their long-run financial plan is to add an
additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4).
Then they plan to make 3 equal annual contributions in each of the
following years, t = 5, 6, and 7. They expect their investment account
to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to
cover Ellen's anticipated college costs?
a.
b.
c.
d.
e.
$1,965.21
$2,068.64
$2,177.51
$2,292.12
$2,412.76
Chapter 5: Time Value of Money
M/C Problems
Page 171
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
CHAPTER 5
ANSWERS AND SOLUTIONS
1.
(5-2) Compounding
F J
Answer: a
EASY
2.
(5-2) Compounding
F J
Answer: b
EASY
3.
(5-2) Compounding
F J
Answer: a
EASY
4.
(5-2) Compounding
F J
Answer: b
EASY
5.
(5-2) Compounding
F J
Answer: a
EASY
6.
(5-2) Compounding
F J
Answer: b
EASY
7.
(5-2) Compounding
F J
Answer: a
EASY
8.
(5-2) Compounding
F J
Answer: b
EASY
9.
(5-2) Compounding
F J
Answer: a
EASY
10.
(5-2) Compounding
F J
Answer: b
EASY
11.
(5-3) PV versus FV
C J
Answer: b
EASY
12.
(5-3) PV versus FV
C J
Answer: a
EASY
13.
(5-3) PV versus FV
C J
Answer: a
EASY
14.
(5-3) PV versus FV
C J
Answer: b
EASY
15.
(5-16) Effective annual rate
C J
Answer: b
EASY
16.
(5-16) Effective annual rate
C J
Answer: a
EASY
17.
(5-2) Compounding
C J
Answer: b
MEDIUM
18.
(5-2) Compounding
C J
Answer: a
MEDIUM
19.
(5-2) Comparative compounding
C J
Answer: a
MEDIUM
Answer: b
MEDIUM
Work out the numbers with a calculator:
PV
1000
FVA =
$1,710.34
Rate on A
5%
2 × FVA = $3,420.68
Rate on B
12%
FVB =
$3,478.55
Years
11
FVB > 2 × FVA, so TRUE
20.
(5-2) Comparative compounding
C J
Work out the numbers with a calculator:
PV
1000
FVA =
$1,710.34
Rate on A
5%
2 × FVA = $3,420.68
Rate on B
12%
FVB =
$3,478.55
Years
11
FVB > 2 × FVA, so FALSE
Page 172
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
21.
(5-3) PV of a sum
C J
Answer: a
MEDIUM
22.
(5-3) PV of a sum
C J
Answer: b
MEDIUM
23.
(5-9) PV of an annuity
C J
Answer: a
MEDIUM
One could make up an example and see that the statement is true. Alternatively, one could simply
recognize that the PV of an annuity declines as the discount rate increases and recognize that more
frequent compounding increases the effective rate.
24.
(5-9) PV of an annuity
C J
Answer: b
MEDIUM
One could make up an example and see that the statement is false. Alternatively, one could simply
recognize that the PV of an annuity declines as the discount rate increases and recognize that more
frequent compounding increases the effective rate.
25.
(5-15) Periodic and nominal rates C J
Answer: a
MEDIUM
26.
(5-15) Periodic and nominal rates C J
Answer: b
MEDIUM
27.
(5-16) Effective and nominal rates
C J
Answer: a
MEDIUM
28.
(5-16) Effective and nominal rates
C J
Answer: b
MEDIUM
29.
(5-18) Amortization
C J
Answer: b
MEDIUM
30.
(5-18) Amortization
C J
Answer: a
MEDIUM
31.
(5-18) Amortization
C J
Answer: a
MEDIUM
32.
(5-18) Amortization
C J
Answer: b
MEDIUM
33.
(5-18) Amortization
C J
Answer: b
HARD
There is no reason to think that this statement would always be true. The portion of the payment
representing interest declines, while the portion representing principal repayment increases.
Therefore, the statement is false. We could also work out some numbers to prove this point. Here's
an example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is
not equal to the principal repayment component except at the high interest rate.
Original loan
Rate
Life
Payment
1
2
3
Beg. Balance Interest
$1,000.00 $100.00
$697.89
$69.79
$365.56
$36.56
Chapter 5: Time Value of Money
$1,000
10%
3
$402.11
Original loan
Rate
Life
Payment
Principal End. Bal.
$302.11 $697.89
$332.33 $365.56
$365.56
$0.00
Answers
1
2
3
Beg. Balance
$1,000.00
$773.52
$453.15
$1,000
41.45%
3
$640.98
Interest
$414.50
$320.62
$187.83
Principal End. Bal.
$226.48 $773.52
$320.36 $453.15
$453.15
$0.00
Page 173
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
34.
(5-18) Amortization
C J
Answer: a
HARD
This statement is true. The portion of the payment representing interest declines, while the portion
representing principal repayment increases. The interest portion could be equal to, greater than, or
less than the principal portion. We can work out some numbers to prove this point. Here's an
example for a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is less
than the principal at 10%, equal at about 41.45%, and greater at rates above 41.45%.
Original loan
Rate
Life
Payment
1
2
3
Beg. Balance Interest
$1,000.00 $100.00
$697.89
$69.79
$365.56
$36.56
$1,000
10%
3
$402.11
Original loan
Rate
Life
Payment
Principal End. Bal.
$302.11 $697.89
$332.33 $365.56
$365.56
$0.00
1
2
3
$1,000
41.45%
3
$640.98
Beg. Balance
$1,000.00
$773.52
$453.15
Interest
$414.50
$320.62
$187.83
Principal End. Bal.
$226.48 $773.52
$320.36 $453.15
$453.15
$0.00
35.
(5-1) Time lines
F J
Answer: b
MEDIUM
36.
(5-1) Time lines
F J
Answer: d
MEDIUM
37.
(5-1) Time lines
F J
Answer: c
MEDIUM
38.
(5-1) Time lines
F J
Answer: e
MEDIUM
39.
(5-3) Effects of factors on PVs
C J
Answer: b
MEDIUM
40.
(5-3) Effects of factors on PVs
C J
Answer: b
MEDIUM
41.
(5-6) Annuities
F J
Answer: d
MEDIUM
42.
(5-6) Annuities
F J
Answer: c
MEDIUM
43.
(5-16) Quarterly compounding
C J
Answer: c
MEDIUM
44.
(5-16) Quarterly compounding
C J
Answer: d
MEDIUM
45.
(5-18) Amortization
C J
Answer: c
MEDIUM
a, d, and e can be ruled out as incorrect by simple reasoning. b is also incorrect because interest in
the first year would be Loan amount × interest rate regardless of the life of the loan, so the interest
payment would be identical for the first payment. Think about the situation whe re r = 0%, statement
c is the "most logical guess." One could also set up an amortization schedule and change the numbers
to confirm that only c is correct.
46.
(5-18) Amortization
C J
Answer: d
MEDIUM
a, c, and e are obviously incorrect. b is also incorrect because interest in the first year would be Loan
amount × interest rate regardless of the life of the loan. That makes d the "most logical guess." One
could also set up an amortization schedule and change the numbers to confirm that only d is corre ct.
47.
(5-18) Amortization
C J
Answer: b
MEDIUM
b is the correct answer. Thinking through the question, the other answers can all be eliminated. One
could also set up an amortization schedule to prove that only statement b is correct.
Page 174
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
48.
(5-18) Amortization
C J
Answer: e
MEDIUM
e is the correct answer. Thinking through the question, the other answers can all be eliminated. One
could also set up an amortization schedule to prove that only statement e is correct.
49.
(5-18) Amortization
C J
Answer: b
MEDIUM
b is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we
could set up an example to see:
Loan
Rate
Periodic rate
100000
10%
0.008333333
Payment
-$877.57
Interest as % of total #360 payment:
1%
Principal as % of total #360 payment 99%
50.
(5-18) Amortization
Term
Periods/Year
Total periods
30
12
360
Interest, Month 1
Interest, Month 360
Principal, Month 360
C J
$833.33
$7.25
$870.32
Answer: b
MEDIUM
b is correct. a is clearly wrong, as are c and d. It is not obvious whether e is correct or not, but we
could set up an example to see:
Loan
Rate
Periodic rate
100000
10%
0.00833333
Payment
Interest as % of total payment:
51.
Term
Periods/Year
Total periods
30
12
360
-$877.57
Interest Month 1
95%, which is much larger than 10%.
(Comp.) Time value concepts
C J
$833.33
Answer: a
MEDIUM
A dominates B because it provides the same total amount, but it comes faster, hence it can earn more
interest over the 10 years. A also dominates C and E for the same re ason, and it dominates D because
with D no interest whatever is earned. We could also do these calculations to answer the question:
A
B
C
D
E
52.
$4,382.79
$4,081.59
$4,280.81
$2,500.00
$3,984.36
Largest
(Comp.) Time value concepts
EFF%
10.00%
NOM% 9.76%
10
C J
250
125
125
2500
250
Answer: d
MEDIUM
A is smaller than E and B is smaller than C because the money comes in later. A is smaller than B
because a larger annuity is received later. So, now the choice comes down to either A or D . Since all
of D is received at the end, this is the logical choice. We could also do these calculations to answer
the question:
A
B
C
D
E
$1,536.14
$1,573.63
$1,650.44
$963.86
$1,689.76
Chapter 5: Time Value of Money
EFF%
10.00%
NOM% 9.76%
Smallest
Answers
10
250
125
125
2500
250
Page 175
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
53.
(Comp.) Time value concepts
C J
Answer: d
MEDIUM
54.
(Comp.) Time value concepts
C J
Answer: e
MEDIUM
55.
(Comp.) Time value concepts
C J
Answer: c
MEDIUM
56.
(Comp.) Time value concepts
C J
Answer: d
MEDIUM
57.
(Comp.) Time value concepts
C J
Answer: a
MEDIUM
58.
(Comp.) Time value concepts
C J
Answer: b
MEDIUM
59.
(Comp.) Annuities
C J
Answer: d
MEDIUM
60.
(Comp.) Annuities
C J
Answer: a
MEDIUM
61.
(5-14) Solving for I: uneven CFs
C J
Answer: c
HARD
62.
(5-14) Solving for I: uneven CFs
C J
Answer: e
HARD
63.
(5-16) Effective annual rate
C J
Answer: e
HARD
By inspection, we can see that e dominates a and b, and that c dominates d because, with the same
interest rate, the account with the most frequent compounding has the highest EFF%. Thus, the
correct answer must be either e or c. Moreover, we can see by inspection that since c and e have the
same compounding frequency yet e has the higher nominal rate, e must have the higher EFF%. You
could also prove that e is the correct choice by calculating the EFF%s:
a.
b.
c.
d.
e.
64.
8.300% = (1+0.08/12)12-1
8.000% = (1+0.08/1)1-1
7.250% = (1+0.07/365)365-1
7.229% = (1+0.07/12)12-1
8.328% = (1+0.08/365)365-1
(5-16) Effective annual rate
C J
Answer: d
HARD
By inspection, we can see that b must have a lower EFF% than either a or e because they all pay the
same nominal rate but b is compounded least frequently. Similarly, c and d pay the same rate, but d is
compounded less frequently, hence d must have the lower EFF%. So, the correct answer must be
either b or d. It is not obvious which of these two has the lower EFF%, so we must do a quick
calculation to determine the correct response. As the following calculations show, d is the correct
answer.
a.
b.
c.
d.
e.
Page 176
8.300% = (1+0.08/12)12-1
8.000% = (1+0.08/1)1-1
7.250% = (1+0.07/365)365-1
7.229% = (1+0.07/12)12-1
8.328% = (1+0.08/365)365-1
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
65.
(5-16) Effective annual rate
C J
Answer: e
HARD
By inspection, we can see that e dominates b, c, and d because, with the same interest rate, the
account with the most frequent compounding has the highest EFF%. Thus, the correct answer must be
either a or e. However, we cannot tell by inspection whether a or e provides the higher EFF%. We
know that with one compounding period a’s EFF% is 6.1%, so we can calculate e's EFF%. It is
6.183%, so e is the correct answer.
a. = (1+0.061/12)12-1 = 6.100%
e. = (1+0.06/365)365-1 = 6.183%
66.
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
67.
68.
69.
70.
Answer: d
EASY
C J
Answer: a
EASY
C J
Answer: a
EASY
C J
Answer: c
EASY
10
6.5%
$2,000
$0
$3,754.27
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
C J
5
3.5%
$1,500
$0
$1,781.53
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
EASY
6
5.5%
$500
$0
$689.42
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
Answer: d
8
8.5%
$125
$0
$240.08
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
C J
5
6.0%
$225.00
$0.00
$301.10
Chapter 5: Time Value of Money
Answers
Page 177
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
71.
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
72.
73.
74.
75.
76.
77.
Page 178
C J
Answer: b
EASY
C J
Answer: b
EASY
C J
Answer: b
EASY
C J
Answer: a
EASY
C J
Answer: a
EASY
10
5.5%
$0
$1,000.00
$585.43
(5-3) PV of a lump sum
N
I/YR
PMT
FV
PV
EASY
25
3.5%
$500
$0
$1,181.62
(5-3) PV of a lump sum
N
I/YR
PMT
FV
PV
Answer: b
25
3.5%
$1,000
$0
$2,363.24
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
C J
75
5.0%
$100.00
$0.00
$3,883.27
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
EASY
75
3.5%
$1.00
$0.00
$13.20
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
Answer: c
8
7.5%
$525.00
$0.00
$936.33
(5-2) FV of a lump sum
N
I/YR
PV
PMT
FV
C J
8
5.5%
$0
$1,000.00
$651.60
Answers
Chapter 5: Time Value of Money
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
78.
(5-3) PV of a lump sum
N
I/YR
PMT
FV
PV
79.
80.
81.
82.
83.
84.
C J
Answer: b
EASY
C J
Answer: b
EASY
C J
Answer: d
EASY
C J
Answer: d
EASY
C J
Answer: b
EASY
10
$3,000.00
$0
$5,000.00
5.24%
(5-4) Growth rate
N
PV
PMT
FV
I/YR
EASY
5
$747.25
$0
$1,000.00
6.00%
(5-4) Finding I
N
PV
PMT
FV
I/YR
Answer: e
10
4.25%
$0
$4,500.00
$2,967.92
(5-4) Finding I
N
PV
PMT
FV
I/YR
C J
5
4.25%
$0
$2,500.00
$2,030.30
(5-3) PV of a lump sum
N
I/YR
PMT
FV
PV
EASY
25
5.5%
$0
$5,000
$1,311.17
(5-3) PV of a lump sum
N
I/YR
PMT
FV
PV
Answer: e
50
7.5%
$0
$20,000
$537.78
(5-3) PV of a lump sum
N
I/YR
PMT
FV
PV
C J
10
$0.50
$0
$2.20
15.97%
Chapter 5: Time Value of Money
Answers
Page 179
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
85.
(5-4) Growth rate
N
PV
PMT
FV
I/YR
86.
87.
88.
89.
90.
91.
Page 180
C J
Answer: e
EASY
C J
Answer: d
EASY
C J
Answer: e
EASY
C J
Answer: e
EASY
C J
Answer: c
EASY
6.0%
$10,000.00
$0
$30,000.00
18.85
(5-7) FV of ordinary annuity
N
I/YR
PV
PMT
FV
EASY
8.0%
$5,000.00
$0
$9,140.20
7.84
(5-5) Finding N
I/YR
PV
PMT
FV
N
Answer: e
9.0%
$3.50
$0
$10.50
12.75
(5-5) Finding N
I/YR
PV
PMT
FV
N
C J
4.0%
$2,500.00
$0
$5,000.00
17.67
(5-5) Finding N
I/YR
PV
PMT
FV
N
EASY
3.8%
$5,000.00
$0
$15,000.00
29.46
(5-5) Finding N
I/YR
PV
PMT
FV
N
Answer: b
5
$1.50
$0
$3.20
16.36%
(5-5) Finding N
I/YR
PV
PMT
FV
N
C J
3
5.2%
$0.00
$4,200
$13,266.56
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
92.
(5-7) FV of ordinary annuity
N
I/YR
PV
PMT
FV
93.
94.
95.
96.
Answer: a
EASY
C J
Answer: a
EASY
3
5.2%
$0.00
$7,000
$23,261
2
$3,500
3
$3,500
4
FV = $16,112
C J
Alternative setup:
0
1
$7,000
$7,000
Answer: c
2
$7,000
EASY
3
$7,000
FV = $23,261
C J
Answer: e
EASY
C J
Answer: e
EASY
10
5.5%
$2,700
$0.00
$20,352
(5-9) PV of ordinary annuity
N
I/YR
PMT
FV
PV
C J
Alternative setup:
0
1
$3,500
$3,500
(5-9) PV of ordinary annuity
N
I/YR
PMT
FV
PV
97.
4
5.7%
$0.00
$3,500
$16,112
(5-8) FV of annuity due
BEGIN Mode
N
I/YR
PV
PMT
FV
EASY
5
8.5%
$0.00
$3,100
$18,369
(5-8) FV of annuity due
BEGIN Mode
N
I/YR
PV
PMT
FV
Answer: c
2
6.2%
$0.00
$8,200
$16,908
(5-7) FV of ordinary annuity
N
I/YR
PV
PMT
FV
C J
5
4.5%
$4,700
$0.00
$20,633
Chapter 5: Time Value of Money
Answers
Page 181
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
98.
(5-9) PV of ordinary annuity
N
I/YR
PMT
FV
PV
99.
100.
101.
EASY
C J
Answer: e
EASY
C J
Answer: b
EASY
C J
Answer: a
EASY
C J
Answer: b
EASY
C J
Answer: a
EASY
20
5.0%
$5,000
$0.00
$62,311
(5-9) PV of ordinary annuity
N
I/YR
PMT
FV
PV
Answer: e
3
5.5%
$2,500
$0.00
$6,744.83
(5-9) PV of ordinary annuity
N
I/YR
PMT
FV
PV
C J
30
7.25%
$50,000
$0.00
$605,183
(5-9) PV of annuity due
BEGIN Mode
N
5
I/YR
5.5%
PMT
$2,500
FV
$0.00
PV
$11,262.88
102.
(5-11) PV of a perpetuity
I/YR
PMT
PV
103.
(5-11) Return on a perpetuity
Cost (PV)
PMT
I/YR
104.
5.0%
$250
$5,000
$950
$85
8.95%
(5-9) PV of annuity due
BEGIN Mode
N
I/YR
PMT
FV
PV
Page 182
C J
Answer: c
MEDIUM
3
5.5%
$550
$0.00
$1,565.48
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
105.
(5-9) PV of annuity due
C J
Answer: c
MEDIUM
C J
Answer: d
MEDIUM
C J
Answer: d
MEDIUM
C J
Answer: b
MEDIUM
C J
Answer: b
MEDIUM
(5-9) PV of ord. ann. & end. pmt. C J
Answer: e
MEDIUM
BEGIN Mode
N
I/YR
PMT
FV
PV
106.
(5-9) PV of annuity due
BEGIN Mode
N
I/YR
PMT
FV
PV
107.
5
4.5%
$5,000
$0.00
$22,938
20
5.25%
$75,000
$0.00
$963,213
(5-9) PV of annuity due
BEGIN Mode
N
25
I/YR
5.15%
PMT
$85,000
FV
$0.00
PV
$1,240,960
108.
(5-9) PV of annuity due
BEGIN Mode
N
I/YR
PMT
FV
PV
109.
(5-9) PV of annuity due
BEGIN Mode
N
I/YR
PMT
FV
PV
110.
25
7.5%
$25,000
$0.00
$299,574
N
I/YR
PMT
FV
PV
15
7.5%
$25,000
$0.00
$237,229
4
5.0%
$2,250
$3,000
$10,446
Chapter 5: Time Value of Money
Alternative setup:
0
1
$2,250
2
$2,250
3
$2,250
$2,250
$2,250
$2,250
4
$2,250
$3,000
$5,250
PV = $10,446.50
Answers
Page 183
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
111.
(5-10) Ord. annuity payments
N
I/YR
PV
FV
PMT
112.
113.
Answer: a
MEDIUM
C J
Answer: d
MEDIUM
C J
Answer: c
MEDIUM
C J
Answer: c
MEDIUM
C J
Answer: d
MEDIUM
C J
Answer: a
MEDIUM
20
8.25%
$275,000
$0.00
$28,532
(5-10) Ord. annuity payments
N
I/YR
PV
FV
PMT
C J
25
7.5%
$375,000
$0.00
$33,641.50
(5-10) Annuity due payments
BEGIN Mode
N
25
I/YR
7.5%
PV
$375,000
FV
$0.00
PMT
$31,294.42
114.
(5-10) Annuity due payments
BEGIN Mode
N
I/YR
PV
FV
PMT
115.
4
6.5%
$100,000
$0.00
$27,409
(5-10) Annuity due payments
BEGIN Mode
N
20
I/YR
8.25%
PV
$275,000
FV
$0.00
PMT
$26,357.92
116.
(5-10) Finding annuity periods
I/YR
PV
PMT
FV
N
Page 184
7.5%
$375,000
$35,000
$0.00
22.50
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a
license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
117.
(5-10) Finding annuity periods
I/YR
PV
PMT
FV
N
118.
119.
120.
121.
122.
123.
C J
Answer: c
MEDIUM
C J
Answer: b
MEDIUM
C J
Answer: a
MEDIUM
C J
Answer: e
MEDIUM
C J
Answer: b
MEDIUM
12
$120,000
$15,000
$0.00
8.41%
(5-11) Payments on a perpetuity
Cost (PV)
I/YR
PMT
MEDIUM
20
$15,000,000
$1,050,000
$0.00
3.44%
(5-10) Finding I: annuity due
BEGIN Mode
N
PV
PMT
FV
I/YR
Answer: e
20
$2,550,000
$250,000
$0.00
7.49%
(5-10) Finding I: annuity
N
PV
PMT
FV
I/YR
C J
5.5%
$500,000
$45,000
$50,000
17.22
(5-10) Finding I: annuity
N
PV
PMT
FV
I/YR
MEDIUM
6.5%
$500,000
$40,000
$0.00
22.86
(5-10) Finding annuity due periods
BEGIN Mode
I/YR
PV
PMT
FV
N
Answer: b
7.50%
$300,000
$35,000
$25,000
14.96
(5-10) Finding annuity due periods
BEGIN Mode
I/YR
PV
PMT
FV
N
C J
$1,250
6.5%
$81.25
Chapter 5: Time Value of Money
Multiply Cost by I/YR.
Answers
Page 185
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license distributed with a certain product or service or otherwise on a password-protected website for classroom use.
124.
(5-12) PV of uneven cash flows
C J
Answer: e
MEDIUM
I/YR = 6.25%
CFs:
PV of CFs:
PV = $505.30
PV = $505.30
0
$0
$0
1
$75
$71
2
$225
$199
3
$0
$0
4
$300
$235
Found using the Excel NPV function.
Found by summing individual PVs.
You can find the individual PVs and sum them. Alternately, you can automate the process using Excel or a
calculator, by inputting the data into the cash flow register and pressing the NPV key.
125.
(5-12) PV of uneven cash flows
C J
Answer: c
MEDIUM
Answer: d
MEDIUM
I/YR = 12.0%
CFs:
PV of CFs:
PV = $10,747
PV = $10,747
PV = $10,747
126.
0
$0
$0
1
$1,500
$1,339
2
$3,000
$2,392
3
$4,500
$3,203
4
$6,000
$3,813
Found using the Excel NPV function.
Found by summing individual PVs.
Found using the calculator NPV key.
(5-12) PV of uneven cash flows
C J
I/YR = 8.0%
CFs:
PV of CFs:
PV = $9,233
PV = $9,233
127.
0
$750
1
$2,450
2
$3,175
3
$4,400
$750
$2,269 $2,722 $3,493
Found by summing individual PVs.
Found with a calculator or Excel to automate the process. With a calculator, input the
cash flows and I into the cash flow register, then press the NPV key.
(5-12) PV of uneven cash flows
C J
Answer: a
MEDIUM
I/YR = 6.0%
CFs:
PV of CFs:
PV = $5,987
PV = $5,987
PV = $5,987
Page 186
0
$0
$0
1
$1,000
$943
2
$2,000
$1,780
3
$2,000
$1,679
4
$2,000
$1,584
Found using the Excel NPV function.
Found by summing individual PVs.
Found using the calculator NPV key.
Answers
Chapter 5: Time Value of Money
© 2013 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or ...