Engineering Economic Analysis

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Problems 137

she may expect to receive 8% nominal annual inter- was paid on money not in the account for the full

est, compounded quarterly, throughout the 40 years. 3-month period. How much was in Ann's account at

The engineer believes her income will increase at a the end of 3 years? (Answer: $3912.30)

7% annual rate during her career. She wishes to start 4-83 What is the present worth of a series of equal quar-

with as Iowa deposit as possible to her IRA now and terly payments of $3000 that extends over a period

increase it at a 7% rate each year. Assuming end-of- of 8 years if the interest rate is 10% compounded

year deposits, how much should she deposit the first monthly?

year? 4-84 The first of a series of equal seII}iannualcash flows oc-

4-78 What single amount on April 1, 1998, is equivalent to curs on July 1, 1997, and the last occurs on January 1,

a series of equal, semiannual cash flows of $1000 that 2010. Each cash flow is equal to $128,000. The nom-

starts with a cash flow on January 1, 1996, and ends inal interest rate is 12% compounded semiannually.

with a cash flow on January 1, 2005? The interest rate What single amount on July 1,2001 is equivalent to

is 14% and compounding is quarterly. this cash flow system?

4-79 Paco's saving account earns 13% compounded 4-85 A man buys a car for $3000 with no money down. He

weekly and receives quarterly deposits of $38,000. pays for the car in 30 equal monthly payments with

His first deposit occurred on October 1, 1996, and the interest at 12% per annum, compounded monthly.

last deposit is scheduled for April 1, 2012. Tisha's What is his monthly loan payment?

account earns 13% compounded weekly. Semiannual (Answer: $116.10)

deposits of $18,000 are made into her account, with 4-86

the first one occurring on July 1, 2006, and the last one On January 1, Frank Jenson bought a used car for

occurring on January 1, 2015. What single amount on $4200 and agreed to pay for it as follows: 1/3down

January 1,2007, is equivalent to the sum of both cash payment; the balance to be paid in 36 equal monthly

flow series? payments; the first payment due February 1; an annual.

interest rate of 9%, compounded monthly.

4-80 The first of a series of equal, monthly cash flows of (a) What is the amount of Frank's monthly payment?

$2000 occurred on April 1, 1998, and the last of the (b) During the summer, Frank made enough money

monthly cash flows occurred on February 1, 2000. to cause him to decide to payoff the entire bal-

This series of monthly cash flows is equivalent to a ance due on the car as of October 1. How much

series of semiannual cash flows. The first semiannual did Frank owe on October 1?

cash flow occurred on July 1,2001, and the last semi- On January 1, Laura Brown borrowed $1000 from the I

annual cash flow will occur on January 1,2010. What

4-87 ,II

is the amount of each semiannual cash flow? Use Friendly Finance Company. The loan is to be repaid

a nominal interest rate of 12% with monthly com- by four equal payments, which are due at the end of

pounding on all accounts. March, June, September, and December. If the finance

company charges 18% interest, compounded quar-

4 1 A series of monthly cash flows is deposited into an terly, what is the amount of each payment? What is the "

account that earns 12% nominal interest compounded effective annual interest rate? (Answers: $278.70; II

monthly. Each monthly deposit is equal to $2100. The 19.3%)

first monthly deposit occurred on June 1, 1998 and the ;I

4-88 TheRuleof 78's is a commoDly used method of com- Iu

last monthly deposit will be on January 1,2005. The puting the amount of interest when the balance of a ;i

account (the series of monthly deposits, 12% nominal IIi:

interest, and monthly compounding) also has equiva-

loan is repaid in advance.

!Ir

lent quarterly withdrawals from it. The first quarterly Adding the numbers representing ,illl

withdrawal is equal to $5000 and occurred on Octo- 12 months gives !im

I!

ber 1,1998. The last $5000 withdrawalwill occur on 1 + 2 + 3 + 4 + 5 + ... + 11+ 12= 78

January 1, 2005. How much remains in the account J

after the last withdrawal? If a 12-month loan is repaid at'the ecfofl

4-82 Ann deposits $100 at the end of each month into her one month, for example, the interest the
bank savings account. The bank paid 6% nominal borrower would be charged is 12/78 of the
interest, compounded and paid quarterly. No interest year's interest. If the loan is repaid at the