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4.1 Introduction
4.2 Simple Interest
4.3 Compound Interest
4.4 The Concept of Equivalence
4.5 Notation and Cash-Flow Diagrams and Tables
4.6 Relating Present and Future Equivalent Values of Single Cash Flows
4.7 Relating a Uniform Series (Annuity) to its Present and Future Equivalent Values
4.10 Equivalence Calculations Involving Multiple Formulas
4.11 Uniform (Arithmetic) Gradient of Cash Flows
4.12 Geometric Sequences of Cash Flows
4.14 Nominal and Effective Interest Rates
4.15 Compounding More Often than Once per Year
4.16 Interest Formulas for Continuous Compounding and Discrete Cash Flows
4.17 Case Study – Understanding Economic “Equivalence”
5.3 The Present Worth Method
5.4 The Future Worth Method
Instructions:
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For full credit, begin each calculation with an appropriate formula, show accurate
calculations and appropriate units, and clearly identify your answers. Computer-generated
submissions are recommended (but not required). You can write mathematical equations
in MS Word and export them to pdf file. See
https://support.office.com/en-us/article/Write-insert-or-change-an-equation-1d01cabcceb1-458d-bc70-7f9737722702
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Please be sure your work is neat and legible, not scribbled or squeezed into the white spaces
and margins of the assignment sheet.
Answer all sub questions (if any) of a problem for full credit for that problem.
1. Try Your Skills 4-E
Jonathan borrowed $10,000 at 6% annual compound interest. He
agreed to repay the loan with five equal annual payments at end-of-years 1-5. How much of
each annual payment is interest, and how much principal is there in each annual payment?
(See section 4.4 of the textbook)
2. Try Your Skills 4-J
In 1803, Napoleon sold the Louisiana Territory to the United States
for $0.04 per acre. In 2017, the average value of an acre at this location is $10,000. What
annual compounded percentage increase in value of an acre of land has been experienced? (See
section 4.6 of the textbook)
3. 4-137
When you were born, your grandfather established a trust fund for you in the
Cayman Islands. The account has been earning interest at the rate of 10% per year. If this
account will be worth $100,000 on your 25th birthday, how much did your grandfather
deposit on the day you were born? (See section 4.6 of the textbook)
(a) $4,000
(b) $9,230
(c) $10,000
(d) $10,150
(e) $10,740
4. 4-139
Your monthly mortgage payment (principal plus interest) is $1,500. If you have a
30-year loan with a fixed interest rate of 0.5% per month, how much did you borrow from the
bank to purchase your house? Select the closest answer. (See section 4.7 of the textbook)
(a) $154,000
(b) $180,000
(c) $250,000
(d) $300,000
(e) $540,000
5. 4-32
An outright purchase of $20,000 now (a lump-sum payment) can be traded for 24
equal payments of $941.47 per month, starting one month from now. What is the monthly
interest rate that establishes equivalence between these two payment plans? (See section 4.7 of
the textbook)
6. 4-59
A sum of $10,000 now (time 0) is equivalent to the following cash-flow diagram.
What is the value of $B if the annual interest rate is 4%? (See section 4.10 of the textbook)
7. 4-140
Consider the following sequence of year-end cash flows.
EOY
1
2
3
4
5
Cash Flow
$8,000
$15,000
$22,000
$29,000
$36,000
What is the uniform annual equivalent if the interest rate is 12% per year? (See section 4.11
of the textbook)
(a) $20,422
(b) $17,511
(c) $23,204
(d) $22,000
(e) $12,422
8. 4-142
Bill Mitselfik borrowed $10,000 to be repaid in quarterly installments over the next
five years. The interest rate he is being charged is 12% per year compounded quarterly. What
is his quarterly payment? (See section 4.15 of the textbook)
(a) $400
(b) $550
(c) $650
(d) $800
9. 4-143
Sixty monthly deposits are made into an account paying 6% nominal interest
compounded monthly. If the objective of these deposits is to accumulate $100,000 by the end
of the fifth year, what is the amount of each deposit? (See section 4.15 of the textbook)
(a) $1,930
(b) $1,478
(c) $1,667
(d) $1,430
(e) $1,695
10. Try Your Skills 5-Q
After graduation, you have been offered an engineering job with a
large company that has offices in Tennessee and Pennsylvania. The salary is $55,000 per year
at either location. Tennessee’s tax burden (state and local taxes) is 6% and Pennsylvania’s is
3.07%. If you accept the position in Pennsylvania and stay with the company for 10 years,
what is the FW of the tax savings? Your personal MARR is 10% per year. (See section 5.4 of
the textbook)
11. Try Your Skills 5-S
Refer to the following table of cash flows. What is the annual worth
of these cash flows over 16 years when i = 5% per year? (See section 5.5 of the textbook)
End of year
0
4
8
12
16
Cash flow
$5,000
$5,000
$5,000
$5,000
$5,000
12. 5-22
What are the present worth PW and future worth FW of a 20-year geometric cashflow progression increasing at 2% per year if the first year amount is $1,020 and then interest
rate is 10% per year? (See section 5.4 of the textbook)
Factor
Name
(F/P, i, N)
Single payment
compound amount factor
Moves a single payment to
N periods later in time
(P/F, i, N)
Single payment present
worth factor
Moves a single payment to
N periods earlier in time
(A/F, i, N)
Sinking Fund factor
Takes a single payment
and spreads into a uniform
series over N earlier
periods. The last payment
in the series occurs at the
same time as F.
(F/A, i, N)
Uniform Series
Compound Amount
factor
Takes a uniform series and
moves it to a single value
at the time of the last
payment in the series.
Capital Recovery Factor
Takes a single payment
and spreads it into a
uniform series over N later
periods. The first payment
in the series occurs one
period later than P.
Uniform Series Present
Worth Factor
Takes a uniform series and
moves it to a single
payment one period earlier
than the first payment of
the series.
Arithmetic Gradient
Present Worth Factor
Takes a arithmetic gradient
series and moves it to a
single payment two
periods earlier than the
first nonzero payment of
the series.
Arithmetic Gradient to
Uniform Series Factor
Takes a arithmetic gradient
series and converts it to a
uniform series. The two
series cover the same
interval, but the first
payment of the gradient
series is 0.
(A/P, i, N)
(P/A, i, N)
(P/G, i, N)
(A/G, i, N)
Formula
Purpose
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