Chapter 6 Exam

You are considering an annuity which costs $160,000 today. The annuity pays $17,500 a year at an annual interest rate of 7.50 percent. What is the length of the annuity time period?

16 years

Project A has cash flows of $4,000, $3,000, $0, and $3,000 for Years 1 to 4, respectively. Project B has cash flows of $2,000, $3,000, $2,000, and $3,000 for Years 1 to 4, respectively. Which one of the following statements is correct assuming the discount rate is positive? (No calculations needed)

Project B is worth less today than Project A.

You are paying an effective annual rate of 18.974 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account?

17.50 percent

You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at an APR of 5.6 percent, compounded monthly. What will be your monthly payment?

$1,048.21 PVADue = $55,000 = C({1 − [1/(1 + .056/12)60]}/(.056/12))(1 + .056/12) C = $1,048.21

You need a 30-year, fixed-rate mortgage to buy a new home for $240,000. Your mortgage bank will lend you the money at a 7.5 percent APR for this 360-month loan, with interest compounded monthly. However, you can only afford monthly payments of $850, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. What will be the amount of the balloon payment if you are to keep your monthly payments at $850?

$1,115,840

Sara wants to establish a trust fund to provide $75,000 in scholarships each year and earn a fixed 6.15 percent rate of return. How much money must she contribute to the fund assuming that only the interest income is distributed?

$1,219,512 PV = $75,000 / .0615 PV = $1,219,512

For the next 20 years, you plan to invest $600 a month in a stock account earning 7 percent and $400 a month in a bond account earning 4 percent. When you retire in 20 years, you will combine your money into an account with a return of 5 percent. How much can you withdraw each month during retirement assuming a 30-year withdrawal period?

$2,465.44 FVA = $600{[(1 + .07/12)(20)( 12) − 1]/(.07/12)} + $400{[(1 + .04/12) (20)(12) − 1]/(.04/12)} FVA = $459,265.85 PVA = $459,265.85 = C({1 − [1/(1 + .05/12)(30)(12)]}/(.05/12)) C = $2,465.44

Your employer contributes $50 a week to your retirement plan. Assume that you work for your employer for another 20 years and that the applicable discount rate is 9 percent per year. Given these assumptions, what is this employee benefit worth to you today?

$24,106.15

Jones Stoneware has a liability of $75,000 due four years from today. The company is planning to make an initial deposit today into a savings account and then deposit an additional $10,000 at the end of each of the next four years. The account pays interest of 4.5 percent. How much does the firm need to deposit today for its savings to be sufficient to pay this debt?

$27,016.84 FVA = $10,000[(1.0454 − 1)/.045] FVA = $42,781.91 Additional FV needed = $75,000 − 42,781.91 Additional FV needed = $32,218.09 Initial deposit = $32,218.09/1.0454 Initial deposit = $27,016.84

What is the future value of $1,200 a year for 40 years at 8 percent interest? Assume annual compounding.

$310,868

You are borrowing $17,800 to buy a car. The terms of the loan call for monthly payments for 5 years at 8.6 percent interest. What is the amount of each payment?

$366.05

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $2,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

$37,537.88 GAPV = $2,500{[1 −(1.05/1.075)20]/(.075 − .05)} GAPV = $37,537.88

You just settled an insurance claim that calls for increasing payments over a 10-year period. The first payment will be paid one year from now in the amount of $5,000. The following payments will increase by 3.5 percent annually. What is the value of this settlement to you today if you can earn 6.5 percent on your investments?

$41,422.89 GAPV = 5,000 {[1-(1.035/1.065)^10] / (0.65 - 0.035)} GAPV = $41,422.89

Your grandmother is gifting you $125 a month for four years while you attend college to earn your bachelor's degree. At an annual 6.5 percent discount rate, what are these payments worth to you on the day you enter college?

$5,270.94

You have just won the lottery and will receive $540,000 as your first payment one year from now. You will receive payments for 26 years. The payments will increase in value by 4 percent each year. The appropriate discount rate is 10 percent. What is the present value of your winnings?

$6,906,372

You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $50,000 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent?

$925,925.93 GPPV = $50,000/(.079 − .025) GPPV = $925,925.93

Convert APR to EAR 1. Bank A: 15% compounded annually: 2. Bank B: 15% compounded quarterly: 3. Bank C: 15% compounded daily:

1.) Answer is 15% i=(1+ 0.15/1)^1 - 1 i= 0.15 x 100 i =15 2.) Answer is 15.865 i=(1+ 0.15/4)^4 - 1 i= 0.15865 x 100 i= 15.865 3.) Answer is 16.1798% i=(1+ 0.15/365)^365 - 1 i= 0.161798 x 100 i = 16.1798

Suppose you are looking at the following possible cash flows: • Year 1 CF = $100;• Years 2 and 3 CFs = $200;• Years 4 and 5 CFs = $300.• The required discount rate is 7%. 1. What is the value of the cash flows at year 5? 2. What is the value of the cash flows today? 3. What is the value of the cash flows at year 3?

1.) The answer is $1,226.07 FV = $100 x (1+7%)^4 + $200 x (1+7%)^3 + $200 x (1+7%)^2 + $300 x (1+7%) FV = $1,226.07 2.) The answer is $874.17 PV= $1,226.07 / (1+7%)^5 PV = $874.17 3.) The answer is $1,070.90 FV = $874.17 x (1+7%)^3 FV = $1,070.90

The Pawn Shop loans money at an annual rate of 23 percent and compounds interest weekly. What is the actual rate being charged on these loans?

25.80 percent

You just paid $480,000 for an annuity that will pay you and your heirs $15,000 a year forever. What rate of return are you earning on this policy?

3.125 percent r = $15,000 / $480,000 r= .03125 or 3.125%

You have just purchased a new warehouse. To finance the purchase, you've arranged for a 30-year mortgage loan for 80 percent of the $2,600,000 purchase price. The monthly payment on this loan will be $12,200. What is the effective annual rate on this loan?

5.95 percent

The Wine Press is considering a project which has an initial cash requirement of $187,400. The project will yield cash flows of $2,832 monthly for 84 months. What is the rate of return on this project?

7.04 percent

You want to buy a new sports coupe for $41,750, and the finance office at the dealership has quoted you an 8.6 percent APR loan compounded monthly for 48 months to buy the car. What is the effective interest rate on this loan?

8.95 percent

First Century Bank wants to earn an effective annual return on its consumer loans of 10 percent per year. The bank uses daily compounding on its loans. By law, what interest rate is the bank required to report to potential borrowers?

9.53 percent

You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.75 percent, compounded daily. Loan B offers a rate of 8 percent, compounded semi-annually. Which loan should you select and why?

A; the effective annual rate is 8.06 percent.

Which one of the following compounding periods will yield the lowest effective annual rate given a stated future value at Year 5 and an annual percentage rate of 10 percent?

Annual

You are comparing two annuities that offer regular payments of $2,500 for five years and pay .75 percent interest per month. You will purchase one of these today with a single lump sum payment. Annuity A will pay you monthly, starting today, while annuity B will pay monthly, starting one month from today. Which one of the following statements is correct concerning these two annuities?

Annuity B has a smaller present value than annuity A.

You are comparing two investment options that each pay 6 percent interest, compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate. (No calculations needed.)

Option B has a higher present value at Time 0.

The interest rate that is most commonly quoted by a lender is referred to as the:

annual percentage rate.

The actual interest rate on a loan that is compounded monthly but expressed as an annual rate is referred to as the ________ rate.

effective annual

A perpetuity is defined as:

unending equal payments paid at equal time intervals.