Chapter 4 BCOR 330

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?

FV = $1,200 ×({[1 + (.0615 / 12)]^60 - 1} / (.0615 / 12))× [1 + (.0615)] = $84,478.33

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

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 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 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

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

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

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

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

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

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; PaymentYear 3 = $50,000 + ($50,000 x .0815) = $54,075.00

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

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

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

13.53 percent

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

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

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 9.6 percent compounded semiannually?

9.83 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.

APR = .049 percent ×365 = .1789, or 17.89 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?

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

Which one of the following qualifies as an annuity payment?

Auto loan payment

Which one of the following statements is correct? A. The APR is equal to the EAR for a loan that charges interest monthly. B. The EAR is always greater than the APR. C. The APR on a monthly loan is equal to (1 + monthly interest rate)12- 1. D. The APR is the best measure of the actual rate you are paying on a loan. E. The EAR, rather than the APR, should be used to compare both investment and loan options.

E.

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

E.

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?

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

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?

FV = $2,000 = $1,500 ×(1 + APR)1 APR = 33.33 percent

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?

FV = $86,000 ×(1 +.068)2 = $98,093.66

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?

FV Year 10= [$8,500 (1 + .078)8] + [$9,300 (1 + .078)7] + [$7,100 (1 + .078)4] = $40,822.55

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.

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

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

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.

PV = $3,990 = $50 × (1 - {1 / [1 + (.139 / 12)]t}) / (.139 / 12) t = 224.16 months PV = $3,990 = $60 × (1 - {1 / [1 + (.139 / 12)]t}) / (.139 / 12) t = 127.72 months Additional cost = (224.16 ×$50) - (127.72 ×$60) = $3,545

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?

P = $4.50/.11 = $40.91

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?

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

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

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

Timing of the annuity payments

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.

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

charge interest annually.

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.