Economics Chapter 5 4 Steve Provided For His Old Age until Now

Chapter 5: The Value of Money

151.

Your child’s orthodontist offers you two alternative payment plans. The first plan requires a $4,000

immediate up-

front payment. The second plan requires you to make monthly payments of $137.41, payable

at the end of each

month for 3 years. What nominal annual interest rate is built into the monthly payment

plan?

a. 12.31%

b. 12.96%

c. 13.64%

d. 14.36%

e. 15.08%

152.

Your subscription to Investing Wisely Weekly is about to expire. You plan to subscribe to the magazine for the

rest

of your life, and you can renew it by paying $85 annually, beginning immediately, or you can get a

lifetime

subscription for $850, also payable immediately. Assuming that you can earn 6.0% on your funds and

that the

annual renewal rate will remain constant, how many years must you live to make the lifetime

subscription the better

buy?

a. 7.48

b. 8.80

c. 10.35

d. 12.18

e. 14.33

153.

You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the

24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal

annual interest

rate will you be earning?

a. 7.62%

b. 8.00%

c. 8.40%

d. 8.82%

e. 9.26%

154.

You just deposited $2,500 in a bank account that pays a 4.0% nominal interest rate, compounded quarterly. If

you

also add another $5,000 to the account one year (4 quarters) from now and another $7,500 to the account

two

years (8 quarters) from now, how much will be in the account three years (12 quarters) from now?

a. $15,234.08

b. $16,035.87

c. $16,837.67

d. $17,679.55

e. $18,563.53

155.

Farmers Bank offers to lend you $50,000 at a nominal rate of 5.0%, simple interest, with interest paid

quarterly.

Merchants Bank offers to lend you the $50,000, but it will charge 6.0%, simple interest, with

interest paid at the end

of the year. What’s the difference in the effective annual rates charged by the two

banks?

a. 1.56%

b. 1.30%

c. 1.09%

d. 0.91%

e. 0.72%

156.

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each

of the

next 5 years. By how much would you reduce the amount you owe in the first year?

a. $2,404.91

b. $2,531.49

c. $2,658.06

d. $2,790.96

e. $2,930.51

11.0%

Per. r

0.9167%

157.

Suppose you borrowed $15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of each

of the

next 5 years. How much would you still owe at the end of the first year, after you have made the first

payment?

a. $10,155.68

b. $10,690.19

c. $11,252.83

d. $11,845.09

e. $12,468.51

158.

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with

equal

end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of

principal?

a. 73.67%

b. 77.55%

c. 81.63%

d. 85.93%

e. 90.45%

159.

Your brother’s business obtained a 30-year amortized mortgage loan for $250,000 at a nominal annual rate of

7.0%,

with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes. What will the

interest tax

deduction be for Year 1?

a. $17,419.55

b. $17,593.75

c. $17,769.68

d. $17,947.38

e. $18,126.85

160.

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit

to be

made one year from today. She will invest in a mutual fund that’s expected to provide a return of 7.5%

per year.

She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after

retirement, to

age 90. Under these assumptions, how much can she spend each year after she retires? Her first

withdrawal will

be made at the end of her first retirement year.

a. $58,601

b. $61,686

c. $64,932

d. $68,179

e. $71,588

161.

Steve and Ed are cousins who were both born on the same day, and both turned 25 today. Their grandfather

began

putting $2,500 per year into a trust fund for Steve on his 20th birthday, and he just made a 6th payment

into the

fund. The grandfather (or his estate’s trustee) will make 40 more $2,500 payments until a 46th and

final payment is

made on Steve’s 65th birthday. The grandfather set things up this way because he wants

Steve to work, not be a

“trust fund baby,” but he also wants to ensure that Steve is provided for in his old age.

Until now, the grandfather has been disappointed with Ed, hence has not given him anything. However, they

recently reconciled, and the grandfather decided to make an equivalent provision for Ed. He will make the

first

payment to a trust for Ed today, and he has instructed his trustee to make 40 additional equal annual

payments until

Ed turns 65, when the 41st and final payment will be made. If both trusts earn an annual return

of 8%, how much

must the grandfather put into Ed’s trust today and each subsequent year to enable him to

have the same retirement

nest egg as Steve after the last payment is made on their 65th birthday?

a. $3,726

b. $3,912

c. $4,107

d. $4,313

e. $4,528

162.

After graduation, you plan to work for Dynamo Corporation for 12 years and then start your own business.

You

expect to save and deposit $7,500 a year for the first 6 years (t = 1 through t = 6) and $15,000 annually

for the

following 6 years (t = 7 through t = 12). The first deposit will be made a year from today. In addition,

your

grandfather just gave you a $25,000 graduation gift which you will deposit immediately (t = 0). If the

account earns

9% compounded annually, how much will you have when you start your business 12 years

from now?

a. $238,176

b. $250,712

c. $263,907

d. $277,797

e. $291,687

163.

You are negotiating to make a 7-year loan of $25,000 to Breck Inc. To repay you, Breck will pay $2,500 at

the end

of Year 1, $5,000 at the end of Year 2, and $7,500 at the end of Year 3, plus a fixed but currently

unspecified cash

flow, X, at the end of each year from Year 4 through Year 7. Breck is essentially riskless, so

you are confident the

payments will be made. You regard 8% as an appropriate rate of return on a low risk but

illiquid 7-year loan. What

cash flow must the investment provide at the end of each of the final 4 years, that

is, what is X?

a. $4,271.67

b. $4,496.49

c. $4,733.15

d. $4,969.81

e. $5,218.30

164.

John and Daphne are saving for their daughter Ellen’s college education. Ellen just turned 10 (at t = 0), and

she will

be entering college 8 years from now (at t = 8). College tuition and expenses at State U. are currently

$14,500 a

year, but they are expected to increase at a rate of 3.5% a year. Ellen should graduate in 4 years if

she takes

longer or wants to go to graduate school, she will be on her own. Tuition and other costs will be due

at the

beginning of each school year (at t = 8, 9, 10, and 11).

So far, John and Daphne have accumulated $15,000 in their college savings account (at t = 0). Their long-run

financial plan is to add an additional $5,000 in each of the next 4 years (at t = 1, 2, 3, and 4). Then they plan

to

make 3 equal annual contributions in each of the following years, t = 5, 6, and 7. They expect their

investment

account to earn 9%. How large must the annual payments at t = 5, 6, and 7 be to cover Ellen’s

anticipated college

costs?

a. $1,965.21

b. $2,068.64

c. $2,177.51

d. $2,292.12

e. $2,412.76

Chapter 5: The Value of Money