Finance 326 Chap 5

You have just won the lottery! You can either receive $5,000 a year for 15 years or $50,000 as a lump sum payment today. What is the interest rate on the annuity option?

A. 5.56 percent

The Jones Brothers recently established a trust fund that will provide annual scholarships of $12,000 indefinitely. These annual scholarships can best be described by which one of the following terms?

D. Perpetuity

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?

B. Annuity

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?

B. Annuity due

Which one of the following cannot be computed?

B. Future value of a perpetuity

Today, you are borrowing $13,800 to purchase a car. What will be your monthly payment amount if the loan is for four years at 7.5 percent interest?

C. $333.67

Hughes Motors will sell you a $15,000 car for $380 a month for 48 months. What is the interest rate?

E. 9.94 percent

Hometown Builders is borrowing $150,000 today for five years. The loan is an interest-only loan with an APR of 8.5 percent. Payments are to be made annually. What is the amount of the first annual payment?

A. $12,750.00 Payment Year 1 = $150,000 × 0.085 = $12,750

Sticks and Stuff Furniture is offering a bedroom suite for $3,000. The credit terms are 60 months at $50 per month. What is the interest rate on this offer?

A. 0.00 percent

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?

A. 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?

A. Interest-only

Which one of the following is an example of a perpetuity?

A. Trust income of $1,200 a year forever

Webster Mining is considering the purchase of a new sorting machine. The quote consists of a quarterly payment of $29,600 for seven years at 8 percent interest. What is the purchase price of the equipment?

B. $629,925.66

The Egg House just borrowed $260,000 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 percent. How much of the first annual payment will be used to reduce the principal balance?

B. $9,575.68 Principal payment = $30,375.68 - ($260,000 × 0.08) = $9,575.68

What is the effective annual rate of 10 percent compounded semiannually?

B. 10.25 percent EAR = [1 + (0.10/2)]^2 - 1 = 10.25 percent

If the appropriate discount rate for the following cash flows is 11.7 percent per year, what is the present value of the cash flows? Year Cash Flow 1 $21,600 2 $25,900 3 $38,700 4 $16,200

C. $78,270.77

Scott borrowed $2,500 today. 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):

B. pure discount loan.

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

A. C × {{1 - [1/(1 + r)t]}/r}

Today, you are purchasing a 20-year, 6 percent annuity at a cost of $120,000. The annuity will pay annual payments starting 1 year from today. What is the amount of each payment?

B. $10,462.15

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 required return on this investment is 4.75 percent, how much will you pay for the policy?

B. $210,526.32 PV = $10,000/0.0475 = $210,526.32

Belk Department Store charges a daily rate of 0.01 percent on its store credit cards. What interest rate is the company required by law to report to potential customers?

B. 36.50 percent APR = 0.01 percent × 365 = 36.50 percent

You recently sold an antique car you owned and valued greatly. However, you needed money and agreed to sell the car at a price of $58,000, to be paid in monthly payments of $1,500 each for 48 months. What interest rate did you charge for financing the sale?

D. 11.03 percent

A credit card has a stated interest rate of 14.56 percent. What is the APR if interest is compounded monthly?

D. 14.56 percent The stated rate is the APR.

A new financial services company just opened in your town. To attract customers, it is offering a "9-11" loan special. The company will lend $9 today in exchange for a payment of $11 one year from today. What is the APR on this loan?

D. 22.22 percent FV = $9 × (1 + r)^1 = $11; r = 22.22 percent

Which one of the following statements is true concerning annuities?

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

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?

A. Amortized

A perpetuity in Canada is frequently referred to as which one of the following?

A. Consul

Which of the following characteristics apply to a perpetuity? I. Constant cash flow dollar amount II. Unequal cash flow dollar amount III. Limited time period IV. Infinite time period

B. I and IV only

You want to borrow $40,000 from your local bank to buy a new sailboat. You can afford to make monthly payments of $775, but no more. Assuming monthly compounding, what is the highest rate you can afford on a 60-month APR loan?

C. 6.1 percent

You are comparing three investments, all of which pay $100 a month and have an 8 percent interest rate. 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?

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

Katie's Dinor spent $84,000 to refurbish its current facility. The firm borrowed 80 percent of the refurbishment cost at 9.2 percent interest for five years. What is the amount of each monthly payment?

D. $1,401.49

McClary Tires just decided to save money each year for the next four years to help fund a new building. If it earns 6.5 percent on its savings, how much will the firm have saved at the end of year 4? End of Year Amount Saved 1 $20,000 2 $24,000 3 $28,000 4 $32,000

D. $113,200.39 FV = ($20,000 × 1.065^3) + ($24,000 × 1.065^2) + ($28,000 × 1.065^1) + $32,000 = $113,200.39

The Rent-to-Own Store has a six-year, interest-only loan at 12 percent interest. The firm originally borrowed $125,000. How much will the firm pay in total interest over the life of the loan?

E. $90,000.00 Total interest = $125,000 × 0.12 × 6 = $90,000

Anna pays 1.5 percent interest monthly on her credit card account. When the interest rate on that debt is expressed as if it were compounded only annually, the rate would be referred to as the:

E. effective annual rate.

Cindy is taking out a loan today. The cash amount that she will receive today 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?

E. Pure discount

Which one of the following qualifies as an annuity?

D. Auto loan payment

Given an interest rate of 5.85 percent per year, what is the value at year t = 8 of a perpetual stream of $2,500 payments that begin at year t = 25?

PV t = 24 = $2,500/0.0585 = $42,735.04; PV t = 8 = $42,735.04/(1 + 0.0585)^16 = $17,208.00

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

C. charge interest annually.

Appalachian Bank offers you a $135,000, nine-year term loan at 7.5 percent annual interest. What will your annual loan payment be?

E. $21,163.57

Which one of the following will decrease the present value of an annuity?

E. Decrease in the annuity payment

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 a 9.2 percent APR. What will your monthly payment be?

A. $1,284.13

You want to purchase a new condominium that costs $329,000. Your plan is to pay 20 percent down in cash and finance the balance over 25 years at 6.25 percent. What will be your monthly mortgage payment?

A. $1,736.25

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 for her down payment?

A. $11,542.10

What is the future value of $20 a week for 10 years at 6 percent interest? Assume the first payment occurs at the end of this week.

A. $14,239.14

Janice plans to save $75 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, Kate will have approximately _____ more than Janice.

A. $2,028.39

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?

A. $37,139.58 PV Year 4 = $42,618.52/[1 + (0.07/2)]^4 = $37,139.58

Kurt wants to have $25,000 in an investment account four years from now. The account will pay 0.2 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?

A. $496.75

West Coast Builders is offering preferred stock for sale with a 6.75 percent rate of return. What is the amount of the annual dividend on this stock if the current market price per share is $83.87?

A. $5.66 C = 0.0675 × $83.87 = $5.66

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?

A. $7,546.70

Karl can afford car payments of $235 a month for 48 months. The bank will lend him money to buy a car at 7.75 percent interest. How much money can he afford to borrow?

A. $9,672.48

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

A. 13.53 percent EAR = 0.1440 = [1 + (APR/12)]^12 - 1; APR = 13.53 percent

Radio Shack offers credit to its customers and charges interest of 1.2 percent per month. What is the annual percentage rate?

A. 14.40 percent APR = 1.2 percent × 12 = 14.40 percent

Standards Life Insurance offers a perpetuity that pays annual payments of $100,000. This contract sells for $2,750,000 today. What is the interest rate?

A. 3.64 percent r = $100,000/$2,750,000 = 3.64 percent

You have just purchased a new warehouse. To finance the purchase, you've arranged for a 25-year mortgage for 80 percent of the $1,800,000 purchase price. The monthly payment on this loan will be $10,800. What is the APR? The EAR?

A. 7.67 percent; 7.94 percent

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?

A. Amortized

First Trust offers personal loans at 7.7 percent compounded monthly. Second Bank offers similar loans at 7.75 percent compounded semiannually. Which one of the following statements is correct concerning these loans?

A. The First Trust loan has an effective rate of 7.98 percent. EAR First Trust = [1 + (0.077/12)]^12 - 1 = 7.98 percent; EAR Second Bank = [1 + (0.075/2)]^2 - 1 = 7.90 percent

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:

A. annual percentage rate.

Which of the following will increase the present value of an annuity, all else held constant? I. Increase in the number of payments II. Increase in the interest rate III. Decrease in the interest rate IV. Decrease in the payment amount

B. I and III only

Billingsley, Inc. is borrowing $60,000 for five years at an APR of 8 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?

B. $14,880

Doris's Fashions has just signed a $2.2 million contract. The contract calls for a payment of $0.6 million today, $0.8 million one year from today, and $0.8 million two years from today. What is this contract worth today if the firm can earn 8.2 percent on its money?

B. $2,022,709.37 PV = $0.6m + ($0.8m/1.082) + ($0.8m/1.0822) = $2,022,709.37

Wesson Metals has an outstanding loan that calls for equal annual payments of $9,768.46 over the life of the loan. The original loan amount was $50,000 at an APR of 8.5 percent. How much of the second loan payment is interest?

B. $3,780.93

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

B. 12.00 percent APR = 1.00 × 12 = 12 percent

You have an outstanding loan with an EAR of 14.6 percent. What is the APR if interest is compounded monthly?

B. 13.71 percent

PayDay Loans wants to earn an effective annual return on its consumer loans of 18 percent per year. The bank uses daily compounding on its loans. What interest rate is the bank required by law to report to potential borrowers?

B. 16.56 percent 0.18 = [1 + (APR/365)^365 - 1; APR = 16.56 percent

The Insolvent Insurance Co. will pay you $2,500 a year for 10 years in exchange for $30,000 today. What interest rate will you earn on this annuity?

B. 3.18 percent

You just received a loan offer from Friendly Loans. The company is offering you $5,000 at 14.3 percent interest. The monthly payment is only $100. If you accept this offer, how long will it take you to pay off the loan?

B. 6.37 years

Which one of the following statements concerning annuities is correct?

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

The manager of Gloria's Boutique has approved Carla's application for credit. The maximum payment that has been approved is $65 a month for 24 months. The APR is 15.7 percent. What is the maximum initial purchase that Carla can make given this credit approval?

C. $1,331.42

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

C. $13,097.52

Today, you are borrowing money from your local bank. The loan is to be repaid in one lump sum payment of $15,000 one year from now. How much money are you borrowing today if the APR is 10.6 percent?

C. $13,562.39

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?

C. $2,024.82

Rick is planning to invest the following amounts at 6 percent interest. How much money will he have saved at the end of year 3? End of Year Amount Saved 1 $500 2 $800 3 $900

C. $2,309.80 FV = ($500 × 1.06^2) + ($800 × 1.06^1) + $900 = $2,309.80

If you put up $46,000 today in exchange for a 6.75 percent 15-year annuity, what will the annual cash flow be?

C. $4,971.10

If today is year 0, what is the future value of the following cash flows 10 years from now? Assume an interest rate of 7.8 percent per year. Year Cash Flow 2 $8,500 3 $9,300 6 $7,100

C. $40,822.55 FV Year 10 = [$8,500 × (1 + 0.078)^8] + [$9,300 × (1 + 0.078)^7] + [$7,100 × (1 + 0.078)^4] = $40,822.55

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

C. $54,578.17 PV = ($11,000/1.12) + ($24,000/1.12^2) + ($36,000/1.12^3) = $54,578.17

You just won a contest! You will receive $100,000 a year for 20 years, starting today. If you can earn 12 percent on your investments, what are your winnings worth today?

C. $836,577.69

Currently, you owe the bank $9,800 for a car loan. The loan has an interest rate of 7.75 percent and monthly payments of $310. Your financial situation recently changed such that you can no longer afford these payments. After talking with your banker and explaining the situation, he has agreed to lower the monthly payments to $225 while keeping the interest rate at 7.75 percent. How much longer will it take you to repay this loan than you had originally planned?

C. 15.84 months

Cromwell Enterprises is acquiring Athens, Inc. for $899,000. Athens has agreed to accept annual payments of $210,000 at an interest rate of 8.5 percent. How many years will it take Cromwell Enterprises to pay for this purchase?

C. 5.55 years

Today is your 21st birthday and you just decided to start saving money so you can retire early. Thus, you are going to save $500 a month starting one month from now. You plan to retire as soon as you can accumulate $1 million. If you can earn an average of 8 percent on your savings, how old will you be when you retire?

C. 54.39 years old

Taylor Farms is borrowing $75,000 for three years at an APR of 9 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 Taylor Farms pay in interest over the life of this loan?

D. $13,500.00

You will receive annual payments of $2,400 at the end of each year for 15 years. The first payment will be received in year 6. What is the present value of these payments if the discount rate is 7 percent?

D. $15,585.16

You want to save $200 a month for the next 24 years and hope to earn an average rate of return of 11 percent. How much more will you have at the end of the 24 years if you invest your money at the beginning of each month rather than the end of each month?

D. $2,569.14

Compass Bank is offering 0.8 percent compounded daily on its savings accounts. If you deposit $2,500 today, how much will you have in the account in 15 years?

D. $2,818.74 FV = $2,500 × [1 + (0.008/365)^]15 × 365 = $2,818.74

Eric is considering an investment that will pay $5,000 a year for seven years, starting one year from today. How much should she pay for this investment if she wishes to earn a 13 percent rate of return?

D. $22,113.05

Kris will receive $800 a month for the next five years from an insurance settlement. The interest rate is 4 percent, compounded monthly, for the first two years and 5 percent, compounded monthly, for the final three years. What is this settlement worth to him today?

D. $43,066.22

Your grandfather started his own business 52 years ago. He opened a savings 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 4.5 percent annually. Today, his account is valued at $364,209.11. How much did your grandfather save every three months?

D. $443.13

A preferred stock pays an annual dividend of $6. What is one share of this stock worth to you today if you require a 12 percent rate of return?

D. $50.00 P = $6/0.12 = $50

Popeye's Fried Chicken just took out an 8 percent interest-only loan of $50,000 for three years. 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?

D. $54,000.00 Payment Year 3 = $50,000 + ($50,000 × 0.08) = $54,000

At the end of this month, Les will start saving $150 a month for retirement through his company's retirement plan. His employer will contribute an additional $0.50 for every $1.00 that he saves. If he is employed by this firm for 30 more years and earns an average of 10.5 percent on his retirement savings, how much will Les have in his retirement account 30 years from now?

D. $566,190.22

The Food Store is planning a major expansion for four years from today. In preparation for this, the company is setting aside $35,000 each quarter, starting today, for the next four years. How much money will the firm have when it is ready to expand if it can earn an average of 6.25 percent on its savings?

D. $640,516.63

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

D. 6 percent compounded monthly

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?

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

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

D. Equal annual payments for life

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?

D. Project 2, because the present value of the cash inflows exceeds those of Project 1 by $18,598.33

Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 7.25 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?

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

The stated interest rate is the interest rate expressed:

D. in terms of the interest payment made each period.

Julie is borrowing $12,800 to purchase a car. The loan terms are 36 months at 7.5 percent interest. How much interest will she pay on this loan if she pays the loan as agreed? Round your answer to the nearest whole dollar.

E. $1,534 Total interest paid = ($398.16 × 36) - $12,800 = $1,534 (rounded)

Your grandparents would like to establish a trust fund that would pay annual payments to you and your heirs of $100,000 a year forever. How much do your parents need to deposit into this trust fund today to achieve their goal if the fund can earn 6 percent interest?

E. $1,666,666.67 P = $100,000/0.06 = $1,666,666.67.

Anne plans to save $40 a week for the next five years. She expects to earn 3 percent for the first two years and 5 percent for the last three years. How much will her savings be worth at the end of the five years?

E. $11,708.15

How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $25,000 a year for 30 years? She expects to earn an average rate of return of 13 percent.

E. $187,391.34

You want to buy a new sports coupe for $84,600, and the finance office at the dealership has quoted you a 7.1 percent APR loan for 48 months to buy the car. What will your monthly payments be? What is the effective annual rate on this loan?

E. $2,029.78; 7.34 percent

Steve is considering investing $3,600 a year for 40 years. How much will this investment be worth at the end of the 40 years if he earns an average annual rate of return of 11.6 percent? Assume Steve invests his first payment of the end of this year.

E. $2,471,685.70

Turntable Industrial, Inc. owes your firm $138,600. This amount is seriously delinquent so your firm has offered to arrange a payment plan in the hopes that it might at least collect a portion of this receivable. Your firm's offer consists of weekly payments for one year at an interest rate of 3 percent. What is the amount of each payment?

E. $2,706.33

Amish Bakery needs $210,000 today to fund a new project. The project will not produce any cash flows for two years and thus the firm agreed to a two-year, pure discount loan at 7.5 percent interest. How much will the firm owe on this loan at the time it must be repaid?

E. $242,681.25 FV = $210,000 × (1 + 0.075)2 = $242,681.25

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

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

Slaughter Industries just signed a sales contract with a new customer. What is this contract worth as of the end of year 4 if the following payments will be received and the firm earns 6 percent on its savings? End of Year Amount Saved 1 $84,000 2 $113,000 3 $125,000 4 $130,000

E. $489,512.14 FV = ($84,000 × 1.06^3) + ($113,000 × 1.06^2) + ($125,000 × 1.06^1) + $130,000 = $489,512.14

A recent alumnus of your university gifted money to the school to fund annual scholarships for students in need. The school expects to earn an average rate of return of 5.5 percent and distribute $50,000 annually in scholarships. What was the amount of the gift?

E. $909,090.91 P = $50,000/0.055 = $909,090.91

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

E. 15.75 percent EAR = [1 + (0.149/4)]^4 - 1 = 15.75 percent

PayDay Loans is offering a special on one-year loans. The company will loan you $5,000 today in exchange for one payment of $5,900 one year from now. What is the APR on this loan?

E. 18.00 percent FV = $5,900 = $5,000 × (1 + APR)1; APR = 18 percent

The Men's Warehouse charges 1.6 percent interest per month. What rate of interest are its credit customers actually paying?

E. 20.98 percent EAR = (1 + 0.016)^12 - 1 = 20.98 percent

The Townhouse Galleries offers credit to its customers at a rate of 1.6 percent per month. What is the effective annual rate of this credit offer?

E. 20.98 percent EAR = (1 + 0.016)^12 - 1 = 20.98 percent

Jake owes $3,400 on his credit card. He is not charging any additional purchases because he wants to get this debt paid in full. The card has an APR of 13.9 percent. How much longer will it take him to pay off this balance if he makes monthly payments of $50 rather than $60?

E. 41.79 months

Overnight Trucking recently purchased a new truck costing $150,800. The firm financed this purchase at 8.6 percent interest with monthly payments of $2,100. How many years will it take the firm to pay off this debt?

E. 8.44 years

Which one of the following statements is correct?

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

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

E. Timing of the annuity payments

When comparing savings accounts, you should select the account that has the:

E. highest 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:

E. will be greater than 12.9 percent.

What is the effective annual rate of 6.5 percent compounded quarterly?

EAR = [1 + (0.065/4)]^ 4 - 1 = 6.66 percent