Finance Chapter 5 test questions

A loan that compounds interest monthly has an EAR of 14.40 percent. What is the APR?

EAR = .1440 = [1 + (APR/12)]12- 1 APR = .1353, or 13.53 percent

You have an outstanding loan with an EAR of 14.61 percent. What is the APR if interest is compounded monthly?

EAR = .1461 = [1 + (APR / 12)]12 - 1 APR =.1371, or 13.71 percent

What is the effective annual rate of 8.25 percent compounded quarterly?

EAR = [1 + (.0825 /4)]4- 1 = .0851, or 8.51 percent

What is the effective annual rate of 14.9 percent compounded quarterly?

EAR = [1 + (.149/4)]4- 1 = .1575, or 15.75 percent

Which one of the following is the annuity present value formula?

C ×({1 - [1/(1 + r)t]}/r)

You want to purchase a new condominium that costs $287,500. Your plan is to pay 25 percent down in cash and finance the balance over 15 years at 3.75 percent. What will be your monthly mortgage payment including principal and interest?

$1,568.07 Amount financed = (1 - .25) ×$287,500 = $215,625 PV = $215,625 = C × (1 - {1 / [1 + (.0375 / 12)]180}) / (.0375 / 12) C = $1,568.07

McClary Tires plans to save $20,000, $25,000, $27,500, and $30,000 at the end of each year for Years 1 to 4, respectively. If it earns 3.3 percent on its savings, how much will the firm have saved at the end of Year 4?

$107,130.78

Janice plans to save $80 a month, starting today, for 20 years. Kate plans to save $80 a month for 20 years, starting one month from today. Both Janice and Kate expect to earn an average return of 5.5 percent on their savings. At the end of the 20 years, Janice will have approximately _____ more than Kate.

$159.73 FVJ = $80 ×{[1 + (.055 / 12)]240 - 1} / (.055 / 12) × [1 + (.055 / 12)] = $35,009.92 FVK = $80 ×{[1 + (.055 / 12)]240 - 1} / (.055 / 12) = $34,850.19 Difference = $35,009.92 -34,850.19 = $159.73

You would like to establish a trust fund that would provide annual scholarships of $100,000 forever. How much would you have to deposit today in one lump sum to achieve this goal if you can earn a guaranteed 4.5 percent rate of return?

$2,222,222 P = $100,000/.045 = $2,222,222

Suenette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the end of Year 3. If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3?

$2,468.69

Which one of the following is an ordinary annuity, but not a perpetuity?

$25 paid weekly for 1 year, starting one week from today

Jeffries & Sons is borrowing $95,000 for four years at an APR of 7.05 percent. The principal is to be repaid in equal annual payments over the life of the loan with interest paid annually. Payments will be made at the end of each year. What is the total payment due for Year 3 of this loan?

$27,098.75

ST Trucking just signed a $3.8 million contract. The contract calls for a payment of $1.1 million today, $1.3 million one year from today, and $1.4 million two years from today. What is this contract worth today at a discount rate of 8.7 percent?

$3,480,817.37

Eric is considering an investment that will pay $8,200 a year for five years, starting one year from today. What is the maximum amount he should pay for this investment if he desires a rate of return of 11.2 percent?

$30,154.50

Alexis plans to invest $2,500 a year for 30 years starting at the end of this year. How much will this investment be worth at the end of the 30 years if she earns an average annual rate of return of 9.6 percent?

$381,324.92 FV = $2,500 ×[(1 + .096)30 - 1] / .096 = $381,324.92 References

How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $42,000 a year for 25 years? She expects to earn an average rate of return of 9.75 percent.

$388,683.83

Today, you are purchasing a 20-year, 6 percent annuity at a cost of $48,350. The annuity will pay annual payments starting one year from today. What is the amount of each payment?

$4,215.37 PV = $48,350 = C × {1 - [1 / (1 + .06)20]} / .06 C = $4,215.37

A preferred stock offers a rate of return of 5.45 percent and sells for $78.20? What is the annual dividend amount?

$4.26 C = .0545 ×$78.20 = $4.26

A preferred stock pays an annual dividend of $4.50. What is one share of this stock worth to you today if you require a rate of return of 11 percent?

$40.91 P = $4.50/.11 = $40.91

Karley's setting aside $32,000 each quarter, starting today, for the next three years for an expansion project. How much money will the firm have at the end of the three years if it can earn an average of 5.45 percent on its savings?

$419,766.30 FV = $32,000 ×{[1 + (.0545 / 4)]12 - 1} / (.0545 / 4)× [1 + (.0545 / 4)] = $419,766.30

At the end of this month, Les will start saving $200 a month for retirement through his company's retirement plan. His employer will contribute an additional $.50 for every $1.00 that he saves. If he is employed by this firm for 30 more years and earns an average of 8.25 percent on his retirement savings, how much will he have in his retirement account 30 years from now?

$470,465.70 Total monthly contribution = $200 + (.5 ×$200) = $300 FV = $300 ×{[1 + (.0825 / 12)]360 - 1} / (.0825 / 12) = $470,465.70

Capstone Investments is considering a project that will produce cash inflows of $11,000 at the end of Year 1, $24,000 in Year 2, and $36,000 in Year 3. What is the present value of these cash inflows at a discount rate of 12 percent? $

$54,578.17

Lacey will receive $135,000 a year for 5 years, starting today. If the rate of return is 8.9 percent, what are these payments worth today?

$573,323.90 PV = $135,000×({1 - [1 / (1 + .089)5]} / .089)× (1 + .089) r = $573,323.90

Uptown Insurance offers an annuity due with semiannual payments for 25 years at 6 percent interest. The annuity costs $200,000 today. What is the amount of each annuity payment?

$7,546.70 PV = $200,000 = C × (1 - {1 / [1 + (.06 / 2)]50}) / (.06 / 2)× [1 + (.06 / 2)] C = $7,546.70

Charlene can afford car payments of $185 a month for 48 months. If the interest rate is 5.65 percent, how much money can she afford to borrow?

$7,931.44 PV = $185 × (1 - {1 / [1 + (.0565 / 12)]48}) / (.0565 / 12) = $7,931.44

Industrial Tools owes you $38,600. This amount is seriously delinquent so you have offered to accept weekly payments for one year at an interest rate of 3 percent to settle this debt in full. What is the amount of each payment?

$753.71 PV = $38,600 = C × (1 - {1 / [1 + (.03 / 52)]52}) / (.03 / 52) C = $753.71

Anne plans to save $40 a week, starting next week,for ten years and earn a rate of return of 4.6 percent, compounded weekly. After the ten years, she will discontinue saving and invest her account at 6.5 percent, compounded annually. How long from now will it be before she has accumulated a total of $50,000?

20.32 years FV = $40 ×({[1 + (.046 / 52)]520 - 1} / (.046 / 52)) = $26,395.74 FV = $50,000 = $26,395.74 ×(1 + .065)t t = 10.32 years Total time = 10 + 10.32 = 20.32 years

Standards Life Insurance offers a perpetuity that pays annual payments of $12,000. This contract sells for $250,000 today. What is the interest rate?

4.80 percent r = $12,000/$250,000 = .0480, or 4.80 percent

Which one of the following has the highest effective annual rate?

6 percent compounded daily

Which statement is true? All else equal, an ordinary annuity is more valuable than an annuity due. All else equal, a decrease in the number of payments increases the future value of an annuity due. An annuity with payments at the beginning of each period is called an ordinary annuity. All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity. All else equal, an increase in the number of annuity payments decreases the present value and increases the future value of an annuity.

All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity

Bill just financed a used car through his credit union. His loan requires payments of $275 a month for five years. Assuming that all payments are paid on time, his last payment will pay off the loan in full. What type of loan does Bill have?

Amortized

Travis is buying a car and will finance it with a loan that requires monthly payments of $265 for the next four years. His car payments can be described by which one of the following terms?

Annuity

You are comparing two annuities. Annuity A pays $100 at the end of each month for 10 years. Annuity B pays $100 at the beginning of each month for 10 years. The rate of return on both annuities is 8 percent. Which one of the following statements is correct given this information?

Annuity B has both a higher present value and a higher future value than Annuity A.

Janis just won a scholarship that will pay her $500 a month, starting today, and continuing for the next 48 months. Which one of the following terms best describes these scholarship payments?

Annuity due

Sporting Goods charges .85 percent interest per month. What rate of interest are its credit customers actually paying?

EAR = (1 + .0085)12- 1 = .1069, or 10.69 percent

Round House Furniture offers credit to its customers at a rate of 1.15 percent per month. What is the effective annual rate of this credit offer?

EAR = (1 + .0115)12- 1 = .1471, or 14.71 percent

Dixie's Markets offers credit to its customers and charges interest of 1.2 percent per month. What is the effective annual rate?

EAR = (1 + .012)12- 1 = .1539, or 15.39%

Travis borrowed $10,000 four years ago at an annual interest rate of 7 percent. The loan term is six years. Since he borrowed the money, Travis has been making annual payments of $700 to the bank. Which type of loan does he have?

Interest-only

You just borrowed $3,000 from your bank and agreed to repay the interest on an annual basis and the principal at the end of three years. What type of loan did you obtain?

Interest-only

All else held constant, the future value of an annuity will increase if you:

increase the time period.

Assume a project will produce cash flows of $22,400, $28,700, $30,300, $10,900 at the end of Years 1 to 4, respectively. If the discount rate is 14.7 percent, what is the current value of these cash flows?

PV = $22,400 / 1.147 + $28,700 / 1.1472 + $30,300 / 1.1473 + $10,900 / 1.1474 = $67,721.24

Assume you pay $24,000 today in exchange for an annuity with monthly payments, an APR of 6.75 percent, and a life of 15 years.What is the payment amount?

PV = $24,000 = C ×[(1 - {1 / [1 + (.0675 / 12)]180}) / (.0675 / .12)] C = $212.38

You want to buy a new sports car from Roy's Cars for $51,800. The contract is in the form of a 48-month annuity due at an APR of7.8 percent, compounded monthly. What would be your monthly payment?

PV = $51,800 = C × [(1 - {1 / [1 + (.078 / 12)]48}) / (.078 /.12)] × [1 + (.078 / 12)] C = $1,251.60

You want to buy a new sports coupe for $84,600and the finance office at the dealership has quoted you an APR of 7.1 percent, compounded monthly, for 72 months. How much interest will you pay over the life of the loan assuming you make all payments on a timely basis?

PV = $84,600 = C × [(1 - {1 / [1 + (.071 / 12)]72}) / (.071 /.12)] C = $1,446.41 Total interest = ($1,446.41 × 72) - $84,600 = $19,542

You will receive annual payments of $800 at the end of each year for 12 years. The first payment will be received in Year 3. What is the present value of these payments if the discount rate is 7 percent?

PV2 = $800× ({1 - [1 / (1 + .07)12]} / .07) × (1 + .07) = $6,354.15 PV0 = $6,354.15 / (1 + .07)2 = $5,549.96

What is the value today of $3,600 received at the end of each year for eight years if the first payment is paid at the end of Year 4 and the discount rate is 12 percent?

PV3 = $3,600× ({1 - [1 / (1 + .12)8]} / .12) × (1 + .12) = $17,883.50 PV0 = $17,883.50 / (1 + .12)3 = $12,729.12

Which one of the following features distinguishes an ordinary annuity from an annuity due?

Timing of the annuity payments

Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 6.3 percent interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. Which one of the following statements is correct concerning this purchase?

To compute the initial loan amount, you must use a monthly interest rate.

The Rent-to-Own Store has a six-year, interest-only loan at 7.6 percent interest. The firm originally borrowed $115,000. How much will the firm pay in total interest over the life of the loan?

Total interest = $115,000 ×.076 ×6 = $52,440.00

The Jones Brothers recently established a trust fund that will provide annual scholarships of $12,000 indefinitely. These annual scholarships are:

a perpetuity.

Assume all else is equal. When comparing savings accounts, you should select the account that has the:

highest effective annual rate.

Lee pays 1 percent per month interest on his credit card account. When his monthly rate is multiplied by 12, the resulting answer is referred to as the:

annual percentage rate.

All else held constant, the present value of an annuity will decrease if you:

decrease the annuity payment.

Anna pays .85 percent interest monthly on her credit card account. When the interest rate on that debt is expressed as if it were compounded annually, the rate would be referred to as the:

effective annual rate.

A credit card has an annual percentage rate of 12.9 percent and charges interest monthly. The effective annual rate on this account:

will be greater than 12.9 percent.