Engineering Economic Analysis

82 INTERESTAND EQUIVALENCE

Problems

3-1 In your own words explain thetime value of money.

From your own life (either now or in a situation -that

might occur in your future), provide an example in

which the time value of money would be important.

Magdalen, Miriam, and Mary June were asked to con-

sider two different cash flows: $500 that they could

receive today and $1000 that would be received

3 years from today. Magdalen wanted the $500 dollars

today, Miriam chose to collect $1000 in 3 years, and

Mary June was indifferent between these two options.

Can you offer an explanation of the choice made by

each woman?

A woman borrowed $2000 and agreed to repay it at

the end of 3 years, together with 10% simple interest

per year. How much will she pay 3 years hence?

A $5000 loan was to be repaid with 8% simple annual

interest. A total of $5350 was paid. How long was the

loan outstanding?

Solve the diagram below for the unknown Qassum-

ing a 10% interest rate.

3-2

3-3

3-4

3-5

200

t

0-1-2-3-4

t n= 4

Q

3-6

(Answer: Q=$136.60)

The followingseries of paymentswill repay a present

sum of $5000 at an 8% interest rate. Using single

payment factors, what present sum is equivalent to

this series of payments at a 10%interest rate?

End-of- Year

Year PaYIDent

1 $1400

2 1320

3 1240

4 1160

5 1080

3-7 A man wentto his bank and borrowed $750. He agreed
to repay the sum at the end of 3 years, together with
the interest at 8% per year. How much will he owe
the bank at the end of 3 years? (Answer: $945)

3-8 What sum of money now is equivalentto $8250 two

years hence, if interest is 4% per 6-month period?

(Answer: $7052)

3-9 The local bank offers to pay 5% interest on savings

deposits. In a nearby town, the bank pays 1.25% per 3-

month period (quarterly). A man who has $3000 to put

in a savings account wonders whether the increased

interest paid in the nearby town justifies driving his

car there to make the deposit. Assuming he will leave

all money in the account for 2 years, how much addi-

tional interest would he obtain from the out-of-town

bank over the local bank?

3-10 A sum of money invested at 2% per 6-month period

(semiannually), will double in amount in approxi-

mately how many years? (Answer:171/zyears)

3-11 The Apex Company sold a water softener to Marty

Smith. The price of the unit was $350. Marty asked

for a deferred payment plan, and a contract was writ-

ten. Under the contract, the buyer could delay paying

for the water softener if he purchased the coarse salt

for recharging the softener from Apex. At the end of

2 years, the buyer was to pay for the unit in a lump

sum, with interest at a rate of 1.5% per quarter-year.

According to the contract, if the customer ceased buy-

ing salt from Apex at any time prior to 2 years, the

full payment due at the end of 2 years would auto-

matically become due.

Six months later, Marty decided to buy salt else-

where and stopped buying from Apex, whereupon

Apex asked for the full payment that was to have been

due 18 months hence. Marty was unhappy about this,

so Apex offered as an alternative to accept the $350

with interest at 10% per semiannual period for the

6 months that Marty had been buying salt from Apex.

Which of these alternatives should Marty accept?

Explain.

3-12 The United States recently purchased $1 billion of

30-year zero-coupon bonds from a struggling foreign

nation. The bonds yield 41/z% per year interest.

The zero-coupon bonds pay no interest during their

30-year life. Instead, at the end of 30 years, the

U.S. government is to receive back its $1 billion.

together with interest at4112%per year. A U.S. senator'

objected to the purchase, claiming that the correct in-

terest rate for bonds like this is5lf4%.The result,

he said, was a multimillion dollar gift to the foreign