FIN CH 5

Which one of the following can be classified as an annuity but not as a perpetuity?

Equal annual payments for life

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

C ×({1 - [1/(1 + r)t]}/r)

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

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

The stated interest rate is the interest rate expressed

in terms of the interest payment made each period.

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?

$1,251.60

Katie's Dinor spent $113,800 to refurbish its current facility. The firm borrowed 65 percent of the refurbishment cost at 6.82 percent interest for six years. What is the amount of each monthly payment?

$1,254.73

Appalachian Bank offers you a $30,000, 2-year term loan at an APR of 5.5 percent, compounded monthly. What will be your monthly loan payment?

$1,322.87

The manager of Gloria's Boutique has approved Carla's application for 24 months of credit with maximum monthly payments of $70.If the APR is 14.2 percent, what is the maximum initial purchase that Carla can buy on credit?

$1,455.08

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

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 itearns 3.3 percent on its savings, how much will the firm have saved at the end of Year 4?

$107,130.78

Kristina started setting aside funds three years ago to save for a down payment on a house. She has saved $900 each quarter and earned an average rate of return of 4.8 percent. How much money does she currently have saved?

$11,542.10

Today, you are borrowing money and must repay the lender one year from now with a lump-sum payment of $12,800.How much money are you borrowing if the interest rate is 8.45 percent, compounded monthly?

$11,766.32

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?

$12,729.12

Hometown Builders is borrowing $195,000 today for four years. The loan is an interest-only loan with an APR of 7.65 percent. Payments are to be made annually. What is the amount of the first annual payment?

$14,917.50

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 Janice.

$159.73

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

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

15.39 percent

Today, you are borrowing $7,800 to purchase a car. What will be your monthly payment if the loan is for four years at 6.45 percent interest?

$184.80

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?

$19,542

A local magazine is offering a $2,500 grand prize to one lucky winner. The prize will be paid in four annual payments of $625 each, starting one year after the drawing. How much would this prize be worth to you if you can earn 9 percent on your money?

$2,024.82

Julie is borrowing $14,950 to purchase a car. The loan terms are 48 months at 6.95 percent interest, compounded monthly. How much interest, rounded to the nearest dollar, will she pay on this loan if she pays the loan as agreed?

$2,217

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

You plan to save $200 a month for the next 24 years and hope to earn an average rate of return of 10.6 percent. How much more will you have at the end of the 24 years if you invest your money at the beginning rather than the end of each month?

$2,317.82

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

15.75 percent

Compass Bank is offering an APR of.8 percent, compounded daily, on its savings accounts. If you deposit $2,500 today, how much will you have in the account in 15 years?

$2,818.74

JK's is borrowing $132,000 for three years at an APR of 7.6 percent. The loan calls for the principal balance to be reduced by equal amounts over the life of the loan. Interest is to be paid in full each year. The payments are to be made annually at the end of each year. How much will be paid in interest over the life of this loan?

$20,064

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?

$212.38

Your grandfather started his own business 52 years ago. He opened an investment account at the end of his third month of business and contributed $x. Every three months since then, he faithfully saved another $x. His savings account has earned an average rate of 5.73 percent annually. Today, his account is valued at $289,209.11. How much did your grandfather save every three months assuming he saved the same amount each time?

$226.78

The Egg House just borrowed $660,000 to build a new restaurant. The loan terms call for equal annual payments at the end of each year. The loan is for 15 years at an APR of 8.35 percent. How much of the first annual payment will be used to reduce the principal balance?

$23,653.18

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 (table)

Alfa Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $10,000 per year forever. If the guaranteed rate of return on this investment is 3.6 percent, how much will you pay for the policy?

$277,777.78

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 fromtoday, 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

Jake owes $3,990 on a credit card with an APR of 13.9 percent. How much more will it cost him to pay off this balance if he makes monthly payments of $50 rather than $60? Assume he does not charge any further purchases.

$3,545

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

A 4-year annuity of eight $6,200 semiannual payments will begin 6 years from now, with the first payment coming 6.5 years from now. If the discount rate is 7 percent, compounded semiannually, what is the value of this annuity 4 years from now?

$37,139.58

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

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

Sheet Metals has an outstanding loan that calls for equal annual payments of $12,600.47 over the life of the loan. The original loan amount was $72,000 at an APR of 8.15 percent. How much of the third loan payment is interest?

$4,725.89

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

Assume you can save $8,500 at the end of Year 2, $9,300 at the end of Year 3, and $7,100 at the end of Year 6. If today is Year 0, what is the future value of your savings 10 years from now if the rate of return is 7.8 percent annually?

$40,822.55

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

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

What is the future value of $25 a week for 40 years at 8.5 percent interest? Assume the first payment occurs at the end of this week

$441,710.03

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

Assume your university earns an average rate of return of 5.65 percent on its endowment funds. If a new gift permanently increases annual scholarships by $32,000, what was the amount of the gift?

$566,371.68

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

JK Industries just signed a sales contract with a new customer. JK will receive annual payments in the amount of $62,000, $108,000, $135,000, and $150,000 at the end of Years 1 to 4, respectively. What is this contract worth at the end of Year 4 if the firm earns 4.3 percent on its savings?

$478,639.54

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?

$5,549.96

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?

$52,440.00

Best's Fried Chicken just took out an interest-only loan of $50,000 for three years with an interest rate of 8.15 percent. Payments are to be made at the end of each year. What is the amount of the payment that will be due at the end of Year 3?

$54,075.00

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

Postal Express is considering the purchase of a new sorting machine. The sales quote consists of quarterly payments of $37,200 for five years at 7.6 percent interest. What is the purchase price?

$614,184.40

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?

$67,721.24

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

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

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

Kurt will receive $1,200 a month for five years from an insurance settlement. The first payment was received today. If he invests the full amount of each payment at a guaranteed 6.15 percent rate, how much will he have saved at the end of the five years?

$84,478.33

Kurt wants to have $835,000 in an investment account six years from now. The account will pay .67 percent interest per month.If he saves money every month, starting one month from now, how much will he have to save each month to reach his goal?

$9,062.07

Given an interest rate of 14.6 percent per year, what is the value at t = 8 of a perpetual stream of $1,250 annual payments that begin t =25?

$967.39

The Corner Bakery needs $86,000 today for remodeling. They have obtained a 2-year, pure-discount loan at an interest rate of 6.8 percent, compounded annually. How much must they repay in two years?

$98,093.66

S&S Furniture is offering a bedroom suite for $3,200. The credit terms are 60 months at $55 per month. What is the interest rate on this offer?

1.22 percent

Overnight Trucking recently purchased a new truck costing $219,800. The firm financed this purchase at 6.6 percent interest with monthly payments of $2,435. How many years will it take the firm to pay off this debt?

10.42 years

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

10.69 percent

What effective annual rate can a bank earn on an APR of 10.5 percent, compounded monthly?

11.02 percent

Cromwell is acquiring some land for $1,200,000 in exchange for semiannual payments of $75,000 at an interest rate of 6.35 percent. How many years will it take Cromwell to pay for this purchase?

11.35 years

Your aunt loaned you money at 1.00 percent interest per month. What is the APR of this loan?

12.00 percent

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

13.53 percent

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

13.71 percent

An amortized, 3-year loan has annual payments and an effective annual rate of 14.56 percent. What is the APR?

14.56 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?

14.71 percent

City Loans wants to earn an effective annual return on its consumer loans of 18.9 percent per year. The bank applies daily compounding. What interest rate is the firm required by law to report to potential borrowers?

17.32 percent

Walker's charges a daily rate of .049 percent on its store credit cards. What interest rate is the company required by law to report to potential customers? Assume each quarter has exactly 91.25 days

17.89 percent

You have just won the lottery! You can either receive $6,500 a year for 20 years or $100,000 as a lump sum payment today. What is the interest rate on the annuity option?

2.64 percent

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

Good Guys will pay you $2,500 a year for 10 years in exchange for $31,300 today. What interest rate will you earn on this annuity?

3.89 percent

E-Z Loans is offering a special on one-year loans. The company will loan you $1,500 today with no waiting and no credit check, in exchange for one payment of $2,000 one year from now. What is the APR on this loan?

33.33 percent

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

So you can retire early, you have decided to start saving $500 a month starting one month from now. You plan to retire as soon as you can accumulate $1 million. If you can earn 5 percent on your savings, how many years will it be before you can retire?

44.76 years

You just received a loan offer from Friendly Loans. The company is offering you $5,000 at 9.3 percent interest. The monthlypayment is only $100. If you accept this offer, how long will it take you to pay off the loan?

5.29 years

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

6 percent compounded daily

You want to borrow $4,700 for 24 months and can afford monthly payments of $210, but no more. Assuming monthly compounding, what is the highest APR rate you can afford?

6.80 percent

Bulk Purchases just purchased a new warehouse. To finance the purchase, the firm arranged for a 25-year mortgage for 80 percent of the $1,800,000 purchase price. The monthly payment is $10,800. What is the APR? The EAR?

7.67 percent; 7.94 percent

Recently, you needed money and agreed to sell a car you had inherited at a price of $55,000, to be paid in monthly payments of $1,500 for 42 months. What interest rate did you charge for financing the sale?

7.78 percent

City Motors will sell a $15,000 car for $345 a month for 52 months. What is the interest rate?

8.38 percent

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

8.51 percent

You owe $6,800on a car loan that has an interest rate of 6.75 percent and monthly payments of $310. You lost your job and your new job pays less, so your lender just agreed to lower the monthly payments to $225 while keeping the interest rate at 6.75 percent. How much longer will it take you to repay this loan than you had originally planned?

9.74 months

What is the effective annual rate of 9.6 percent compounded semiannually?

9.83 percent

Which statement is true?

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

Letitia borrowed $6,000 from her bank two years ago. The loan term is four years. Each year, she must repay the bank $1,500 plus the annual interest. Which type of loan does she have?

Amortized

Which one of the following statements concerning annuities is correct?

An annuity due has payments that occur at the beginning of each time period

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

Which one of the following qualifies as an annuity payment?

Auto loan payment

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

increase the time period

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

Which one of the following statements is correct?

The EAR, rather than the APR, should be used to compare both investment and loan options

Chandler Tire Co. is trying to decide which one of two projects it should accept. Both projects have the same start-up costs.Project 1 will produce annual cash flows of $52,000 a year for six years. Project 2 will produce cash flows of $48,000 a year for eight years. The company requires a 15 percent rate of return. Which project should the company select and why?

Project 1, because the present value of its cash inflows exceeds those of Project 2 by $14,211.62

Cindy is taking out a loan today. The cash amount that she is receiving is equal to the present value of the lump sum payment that she will be required to pay two years from today. Which type of loan is this?

Pure discount

First Bank offers personal loans at 7.7 percent compounded monthly. Second Bank offers similar loans at 7.4percent compounded daily. Which one of the following statements is correct concerning these loans? Assume a 365-day year

The First Bank loan has an effective rate of 7.98 percent.

Which one of these is a perpetuity?

Trust income of $1,200 a year forever

You are comparing three investments, all of which pay $100 a month and have an interest rate of 8 percent. One is ordinary annuity, one is an annuity due, and the third investment is a perpetuity. Which one of the following statements is correct given these three investment options?

The present value of the perpetuity has to be higher than the present value of either the ordinary annuity or the annuity due

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.

A perpetuity in Canada is frequently referred to as

a consul.

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

A 30-year home mortgage is a classic example of:

an ordinary annuity

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.

A loan has an APR of 8.5 percent and an EAR of 8.5 percent. Given this, the loan must

charge interest annually.

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

Perpetuities have:

equal payments and an infinite life

Scott borrowed $2,500 today at an APR of 7.4 percent. The loan agreement requires him to repay $2,685 in one lump sum payment one year from now. This type of loan is referred to as a(n):

pure discount loan.

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