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Homework 2 – IMSE 2324 – Instructor: Rafael Cacao
Chapter 3
1 – If a savings bank pays 5.5% interest every 3 months, what are the annual nominal and effective
interest rates? Answer: Nominal: 22% and Effective: 23.88%
2 – A friend was left $50,000 by his uncle. He has decided to put it into a savings account for the next
year. Bank A offered him 2.25% compounded every two months. Bank B offered 2.30% compounded
quarterly. Bank C offered him 3.30% compounded continuously. He wishes to select the Bank that will
give him the highest return on investment. What bank should he select? Answer: Bank A as it has the
best rate: 14.28%. Bank B and Bank C have respectively 9.52% and 3.35%.
3 – If you were to deposit $2000 in a bank that pays 5% nominal interest, compounded continuously, how
much would be in the account at the end of 2 years? Answer: $2210.34
4 – What sum of money now is equivalent to $9,500 in 3 years if interest is 3% per semester? Answer:
$7956.10
5 – A sum of money Q will be received 6 years from now. At a 5% interest rate, the present worth of Q is
$60. At the same interest rate, what would be the value of Q in 10 years? (Answer: In 10 years, Q is
$97.61)
Chapter 4
1 – A man buys a car for $33,000 with no money down. He pays for the car in 48 equal monthly payments
with interest at 9% per year, compounded monthly. What is his monthly loan payment? Answer: $821
2 – Rose recently graduated in engineering. Her employer will give her a raise of $6500 per year if she
passes the FE exam (Fundamentals of Engineering). Over a career of 45 years, what is the present worth
of the raise if the interest rate is 4%? Answer: $134,680
3 – If i = 12%, for what value of B is the present value = 0? Answer: $1094.3
4 – These cash flow transactions are said to be equivalent in terms of economic desirability at an interest
rate of 9% compounded annually. Determine the unknown value A. You must use gradient to calculate
cash flow 2. Answer: $340
5 – For what value of P in the cash flow diagram does the present value equal 0? You must use gradient
Answer: $5,545
6 – Calculate the present value of the following cash flow diagram at 10% interest rate (you must use
gradient): Answer: $11536.20
Chapter 5
1 – A farmer is considering buying a new tractor. He has two choices he feels would meet his needs. One
is smaller than the other. It costs less but is also less capable and will be used more hours to tend the same
amount of farmland. Using the estimates below, which tractor presents the best value? Use 5% interest.
(Answer: PW for A is $25,185 and PW for B is $81,806.8, so should pick B)
2 – The City of Lubbock has decided to buy a new snow removal machine to avert the occasional
snowpocalypse. Thus, the city of Lubbock decided to buy a new snow removal machine. The officials can
choose between two different machines: 1. The Blizzard has a $70,000 first cost, a 20-year life, and $8,000
salvage value. At the end of 9 years, it will need a major overhaul costing $9,000. Annual maintenance and
operating costs are $9,000. 2. The Snow Mower will cost $50,000, has an expected life of 10 years, and
has no salvage value. The annual maintenance and operating costs are expected to be $12,000. Using a
12% interest rate, which machine should be chosen? Use Present Worth Analysis. (Answer: select the
Blizzard as it is the least expensive with a PW of -139,636.80 versus the other with PW of -155,728.)
3 – Dr. Fog E. is retiring and wants to endow a chair of engineering economics at his university. It is expected
that he will need to cover an annual cost of $250,000 forever. What lump sum must he donate to the
university today if the endowment will earn 5% interest? Answer: $5,000,000
4 – A firm wants to sponsor a new engineering lab at a local university. This requires $4M to construct the
lab, $1.5M to equip it, and $750,000 every 6 years for new equipment. What is the required endowment
if the university will earn 8% interest on the funds? Answer: $6,777,957
5 – Which equipment is preferred using PW analysis if the firm’s interest rate is 15%? In PW terms how
great is the difference? PW for A is $-68896.47 and for B is -69758.21. Thus the best option is to not invest
in any.
Homework 3
1 – Compute the EUAB for these cash flows based on a 12% interest rate.
Answer: $39.62
2 – Compute the EUAB for these cash flows based on a 10% interest rate.
Answer: $35.38
3 – For the diagram, compute the value of D that results in a net equivalent uniform annual worth
(EUAW) of 0. Interest rate is 10%
Answer: D = $90.15
4 – An electronics firm invested $50,000 in a precision inspection device. It cost $1500 to operate and
maintain each year. An additional cost of $750 was observed on years 2 and 4 for software updates. The
device was sold after 5 years. The purchasing agent was very fortunate to sell the inspection device for
$40,000. Compute the equivalent uniform annual cost during the 5 years the device was used. Assume
interest at 10% per year. Answer: EUAC = $8,559.47
5 – The manager in a factory is trying to decide between two machines:
Cost
Operation and
Maintenance
Uniform annual benefit
Salvage
Useful life
A
15,000
1,600
B
25,000
400
8,000
3,000
6
13,000
6,000
10 years
For an interest rate of 6%, use annual cash flow analysis to determine which machine should be chosen.
Answer: Machine B
6 – Calculate the internal rate of return for the following investments:
Initial Cost
Annual Benefit
Operations and Maintenance
Salvage Value
Useful Life
$-10,000
$6,000
$4,000
$5,000
8 years
Answer: 16.27%
7 – Calculate the internal rate of return for the following investments:
Initial Cost
Annual Benefit
Operations and Maintenance
Overhaul at year 3
Salvage Value
Useful Life
Answer: 13.43%
$-30,000
$10,000
$2,000
$8,000
$8,000
6 years
8 – For the following diagram, compute the IRR. Answer: 13.23%
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