Assignment 2

IE 432 - Engineering Economics
Assignment 2
Instructor: Dr. Sinan Obaidat

Department of Industrial Engineering
Yarmouk University
© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo

Assignment 2 – Lectures (4 – 6)
© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 1

Problem 1
You borrow $500 from a family member and agree to pay it back in 6 months.
Because you are part of the family, you are only being charged simple interest at
the rate of 0.5% per month. How much will you owe after 6 months? How much
is the interest?

Problem 2
How much interest is payable each year on a loan of $2,000 if the interest rate is
10% per year when half of the loan principal will be repaid as a lump sum at the
end of four years and the other half will be repaid in one lump-sum amount at
the end of eight years?
How much interest will be paid over the eight-year period?

Problem 3
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 the annual payment is interest?
How much principal is there in each annual payment?

Problem 4
A lump-sum loan of $5,000 is needed by Chandra to pay for college expenses.
She has obtained small consumer loans with 12% interest per year in the past to
help pay for college. But her father has advised Chandra to apply for a PLUS
student loan charging only 8.5% interest per year.
If the loan will be repaid in full in five years, what is the difference in total
interest accumulated by these two types of student loans?

Problem 5
(a) You have just invested a one-time amount of $5,000 in a stock-based mutual
fund. This fund should earn (on average) 9% per year over a long period of
time. How much will your investment be worth in 35 years?
(b) A12-cylinder heavy-duty diesel engine will have a guaranteed residual value
of $1,000 in 5 years. Today (year 0) the equivalent worth of this engine is how
much if the interest rate is 9% per year?

Problem 6
A certain college graduate, Sallie Evans, has $24,000 in student-loan debt at the
end of her college career. The interest rate on this debt is 0.75% per month. If
monthly payments on this loan are $432.61, how many months will it take for
Sallie to repay the entire loan?

Problem 7
Let’s say you are intent on receiving $45,000 per year, starting at the end of year
one and continuing over 10 years. A lump-sum of $380,000 invested now (year
0) will allow you to receive your desired annual amount.
What interest rate is required to make this happen?

Problem 8
Twelve payments of $10,000 each are to be repaid monthly at the end of each
month. The monthly interest rate is 2%.
(a) What is the present equivalent of these payments?
(b) Repeat Part (a) when the payments are made at the beginning of the month.
Note that the present equivalent will be at the same time as the first monthly
payment.
(c) Explain why the present equivalent amounts in Parts (a) and (b) are different.

Problem 9
It is estimated that a certain piece of equipment can save $22,000 per year in
labor and materials costs. The equipment has an expected life of five years and
no market value. If the company must earn a 15% annual return on such
investments,
(a) Draw a cash-flow diagram.
(b) How much could be justified now for the purchase of this piece of
equipment?

Problem 10
Consider the accompanying cash-flow diagram.

Problem 11
How much money should be deposited each year for 12 years if you wish to
withdraw $309 each year for five years, beginning at the end of the 14th year?
Let i = 8% per year.

Problem 12
Major overhaul expenses of $5,000 each are anticipated for a large piece of
earthmoving equipment. The expenses will occur at EOY four and will continue
every three years thereafter up to and including year 13. The interest rate is 12%
per year.
a. Draw a cash-flow diagram.
b. What is the present equivalent of the overhaul expenses at time 0?
c. What is the annual equivalent expense during only years 5–13?

Problem 13
Maintenance expenses for a bridge on the Ohio River are estimated to be
$20,000 per year for the first 8 years, followed by two separate $100,000
expenditures in years 12 and 18. The expected life of the bridge is 30 years.
If i = 6% per year, what is the equivalent uniform annual expense over the entire
30-year period?

Problem 14
Transform the cash flows on the left-hand side of the accompanying diagram to
their equivalent amount, F, shown on the right-hand side. The interest rate is 8%
per year.

Problem 15
Determine the value of W on the right-hand side of the accompanying diagram
that makes the two cash-flow diagrams equivalent when i = 12% per year.

Problem 16
What value of T makes these two cash flow diagrams economically equivalent at
8% annual interest?

Problem 17
Compute the effective annual interest rate in each of the following situations.
a. 5.75% nominal interest, compounded quarterly.
b. 5.75% nominal interest, compounded daily.

Problem 18
Determine the current amount of money that must be invested at 12% nominal
interest, compounded monthly, to provide an annuity of $10,000 (per year) for 6
years, starting 12 years from now. The interest rate remains constant over this
entire period of time.

Problem 19
To pay off $50,000,000 worth of new construction bonds when they come due in
20 years, a water municipality must deposit money into a sinking fund.
Payments to the fund will be made quarterly, starting three months from now. If
the interest rate for the sinking fund is 8% compounded quarterly, how much
will each deposit be?

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IE 432 - Engineering Economics

Instructor: Dr. Sinan Obaidat

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 1

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 2

How much interest will be paid over the eight-year period?

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 3

How much of the annual payment is interest?

How much principal is there in each annual payment?

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 4

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 5

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 6

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 7

What interest rate is required to make this happen?

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 8

(a) What is the present equivalent of these payments?

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 9

(a) Draw a cash-flow diagram.

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 10

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 11

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 12

a. Draw a cash-flow diagram.

b. What is the present equivalent of the overhaul expenses at time 0?

c. What is the annual equivalent expense during only years 5–13?

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 13

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 14

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 15

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 16

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 17

a. 5.75% nominal interest, compounded quarterly.

b. 5.75% nominal interest, compounded daily.

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 18

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 19

© Dr. Sinan Obaidat; sinan.obaidat@yu.edu.jo 20

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