a.
PROBLEMS
1. Find the future value (FV) one year from now of a $7,000 invest-
ment at a 3 percent annual compound interest rate. Also, calculate
the FV if the investment is made for two years.
2. Find the FV of $10,000 invested now after five years if the annual
interest rate is 8 percent.
a. What would be the FV if the interest rate is a simple interest
rate?
b. What would be the FV if the interest rate is a compound inter-
est rate?
3. Determine the future values (FVs) if $5,000 is invested in each of
the following situations:
a. 5 percent for ten years
b. 7 percent for seven years
C. 9 percent for four years
4. You are planning to invest $2,500 today for three years at a nomi-
nal interest rate of 9 percent with annual compounding.
a. What would be the future value (FV) of your investment?
b. Now assume that inflation is expected to be 3 percent per year
over the same three-year period. What would be the invest-
ment's FV in terms of purchasing power?
C. What would be the investment's FV in terms of purchasing
power if inflation occurs at a 9 percent annual rate?
5. Find the present value (PV) of $7,000 to be received one year from
now assuming a 3 percent annual discount interest rate. Also calcu-
late the PV if the $7,000 is received after two years.
6. Determine the present values (PVs) if $5,000 is received in the
future (i.e., at the end of each indicated time period) in each of the
following situations:
5 percent for ten years
b. 7 percent for seven years
C. 9 percent for four years
7. Determine the present value (PV) if $15,000 is to be received at the
end of eight years and the discount rate is 9 percent. How would your
answer change if you had to wait six years to receive the $15,000?
8. Determine the future value (FV) at the end of two years of an
investment of $3,000 made now and an additional $3,000 made one
year from now if the compound annual interest rate is 4 percent.
9. Assume you are planning to invest $5,000 each year for six years
and will earn 10 percent per year. Determine the future value
(FV) of this annuity if your first $5,000 is invested at the end of
the first year.
10. Determine the present value (PV) now of an investment of $3,000
made one year from now and an additional $3,000 made two years
from now if the annual discount rate is 4 percent.
11. What is the present value (PV) of a loan that calls for the payment
of $500 per year for six years if the discount rate is 10 percent and the
first payment will be made one year from now? How would your
answer change if the $500 per year occurred for ten years?
12. Determine the annual payment on a $500,000, 12 percent busi-
ness loan from a commercial bank that is to be amortized over a five-
year period.
a.
a.
13. Determine the annual payment on a $15,000 loan that is to be
amortized over a four-year period and carries a 10 percent interest
rate. Prepare a loan amortization schedule for this loan.
14. You are considering borrowing $150,000 to purchase a new
home.
Calculate the monthly payment needed to amortize an 8
percent fixed-rate 30-year mortgage loan.
b. Calculate the monthly amortization payment if the loan in (a)
was for 15 years.
15. Assume a bank loan requires an interest payment of $85 per year
and a principal payment of $1,000 at the end of the loan's eight-year life.
At what amount could this loan be sold for to another bank if
loans of similar quality carried an 8.5 percent interest rate?
That is, what would be the present value (PV) of this loan?
b. Now, if interest rates on other similar quality loans are 10
percent, what would be the PV of this loan?
c. What would be the PV of the loan if the interest rate is 8
percent on similar quality loans?
16. Use a financial calculator or computer software program to
answer the following questions:
a. What would be the future value (FV) of $15,555 invested now
if it earns interest at 14.5 percent for seven years?
b. What would be the FV of $19,378 invested now if the money
remains deposited for eight years and the annual interest rate
is 18 percent?
21. What would be the present value (PV) of a $9,532 annuity for
which the first payment will be made beginning one year from now,
payments will last for twenty-seven years, the annual interest rate is
13 percent, quarterly discounting occurs, and $2,383 is invested at
the end of each quarter?
22. Answer the following questions.
What is the annual percentage rate (APR) on a loan that
charges interest of.75 percent per month?
b. What is the effective annual rate (EAR) on the loan described
in (a)?
23. You have recently seen a credit card advertisement stating that the
annual percentage rate (APR) is 12 percent. If the credit card requires
monthly payments, what is the effective annual rate (EAR) of interest
on the loan?
24. A credit card advertisement states that the annual percentage rate
(APR) is 21 percent. If the credit card requires quarterly payments,
what is the effective annual rate (EAR) of interest on the loan?
25. Challenge Problem (A computer spreadsheet software program
or a financial calculator that can handle uneven cash flow streams
will be needed to solve the following problems.) The following
cash flow streams are expected to result from three investment
opportunities:
a.
YEAR
INVESTMENT
STABLE
$20,000
INVESTMENT
DECLINING
$35,000
INVESTMENT
GROWING
$10,000
3
20,000
20,000
20,000
20,000
30,000
20,000
5,000
0
15,000
20,000
30,000
50,000
4
17. Use a financial calculator or computer software program to
answer the following questions:
a. What is the present value (PV) of $359,000 that is to be received
at the end of twenty-three years if the discount rate is 11 percent?
b. How would your answer change in (a) if the $359,000 is to be
received at the end of twenty years?
18. Use a financial calculator or computer software program to
answer the following questions:
a. What would be the future value (FV) of $7,455 invested annu-
ally for nine years beginning one year from now if the annual
interest rate is 19 percent?
b. What would be the present value (PV) of a $9,532 annuity for
which the first payment will be made beginning one year from
now, payments will last for twenty-seven years, and the annual
interest rate is 13 percent?
19. Use a financial calculator or computer software program to
answer the following questions.
a. What would be the future value (FV) of $19,378 invested now
if the money remains deposited for eight years, the annual
interest rate is 18 percent, and interest on the investment is
compounded semiannually?
b. How would your answer for (a) change if quarterly
compounding were used?
20. Use a financial calculator or computer software program to
answer the following questions.
a. What is the present value (PV) of $359,000 that is to be
received at the end of twenty-three years, the discount rate is
11 percent, and semiannual discounting occurs?
b. How would your answer for (a) change if monthly discount-
ing were used?
a. Find the present values (PVS) at the end of time period zero
for each of these three investments if the discount rate is 15
percent. Find the PVs for each investment using 10 percent
and 20 percent discount rates.
b. Find the future values (FVs) of these three investments at the
end of year-five if the compound interest rate is 12.5 percent.
Find the FVs for each investment using 2.5 percent and 22.5
percent compound rates.
C. Find the PVs of the three investments using a 15 percent
annual discount rate but with quarterly discounting. Find the
PVs for semiannual and monthly discounting for a 15 percent
stated annual rate.
d. Find the FVs of the three investments using a 12.5 percent
annual compound rate but with quarterly compounding.
Find the FVs for semiannual and monthly compounding for a
12.5 percent stated annual rate.
e. Assume that the PV for each of the three investments is $75,000.
What is the annual interest rate (%i) for each investment?
f. Show how your answers would change in (e) if quarterly
discounting takes place.
g. Assume that the FV for each of the three investments is
$150,000. What is the annual interest rate (%i) for each
investment? (Remember that (e) and (g) are independent of
each other.)
h. Show how your answers would change in (g) if quarterly
compounding takes place.
interest rate
basic price that equates the
demand for and supply of
loanable funds in the
financial markets
SUPPLY AND DEMAND FOR LOANABLE FUNDS
Lenders are willing to supply funds to borrowers as long as lenders can earn a satisfactory
return on their loans (i.e., an amount greater than that which was lent). Borrowers will demand
funds from lenders as long as borrowers can invest the funds so as to earn a satisfactory return
above the cost of their loans. Actually, the supply and demand for loan able funds will take place
as long as lenders and borrowers have the expectation of satisfactory returns. Of course, returns
received may differ from those expected because of inflation, failure to repay loans, and poor
investments. Return experiences will, in turn, affect future supply and demand relationships
for loanable funds.
The basic price that equates the demand for and supply of loanable funds in the financial
markets is the interest rate. Figure 8.1 depicts how interest rates are determined in the financial
markets. Graph A shows the interest rate (r) that clears the market by bringing the demand (D)
by borrowers for funds in equilibrium with the supply (S) by lenders of funds. For illustrative
purposes, we have chosen a rate of 5 percent as the cost or price that makes savings equal to
investment (i.e., where the supply and demand curves intersect).
Interest rates may move from an equilibrium level if an unanticipated change or "shock"
changes the demand for, or supply of, loan able funds. For example, an increase in the desire to
invest in business assets because of an expanding economy might cause the demand for loan able
funds to increase or shift upward (i.e., from D, to D.). The result, depicted in Graph B, will be an
increase or rise in interest rates to, say, 6 percent, assuming no immediate adjustment in the
supply of funds. Of course, as higher interest rates become available to savers, savings may
increase, which could cause the supply of loanable funds to increase. A decline in business activity
would be expected to have the opposite impact on interest rates.
Graph C depicts an unanticipated increase in inflation, which leads lenders (suppliers) to
require a higher rate of interest. This is shown by the shift in supply from S, to S, which for illus-
trative purposes shows an increase in the interest rate from 5 percent to 7 percent. At this point,
we have not taken into consideration that borrowers may adjust their demand for loanable funds
because of the likelihood of more costly loans. Graph D depicts the situation that borrowers
(users) may cut back on their demand for loanable funds from D to D, because of the unantici-
pated increase in inflation. For example, this would occur if borrowers felt their higher borrowing
costs could not be passed on to their customers, and thus, the returns on their investments would
be adversely affected by the higher inflation rates. Instead of the unanticipated increase in infla-
tion shock causing the interest rate to rise to 7 percent, the new equilibrium rate where supply
equals demand investment) might be only 6 percent.
CONCEPT CHECK
How are interest rates
determined in the financial
markets?
FIGURE 8.1
Interest Rate Determination in the Financial Markets
Graph A
Graph B
S
S
6%
Interest
Rate(r)
5%
Interest
Rate(r)
D2
D
D
Quantity of Loanable Funds
Quantity of Loanable Funds
Graph
Graph D
S2
S
SI
7%
Interest
Rate (1)
Interest
Rate
6%
D
D
D
Quantity of Loanable Funds
Quantity of Loanable Funds
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