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Chapter 5
The Time Value of Money
Answer Key
- What is the future value of $10,000 on deposit for 5 years at 6% simple interest? A. $7,472. B. $10,303. C. $13,000. D. $13,382.
FV = PV + (PV r t ) ($10,000) + [($10,000 .06) 5] = $13,000.
- How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually? A. $70. B. $80. C. $105. D. $140.
$1000.00 (1.07)^2 = $1,144.90 after 2 years $1,144.90 .07 = $80.
- The concept of compound interest refers to: A. earning interest on the original investment. B. payment of interest on previously earned interest. C. investing for a multiyear period of time. D. determining the APR of the investment.
- When an investment pays only simple interest, this means: A. the interest rate is lower than on comparable investments. B. the future value of the investment will be low. C. the earned interest is nontaxable to the investor. D. interest is earned only on the original investment.
- Approximately how long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually? A. 9 years B. 14 years C. 22 years D. 25 years
$3,000 = $1,000(1.08) n 3 = (1.08) n n = ln(3) / ln(1.08) = 14. or approximately n = 14 years.
- How much will accumulate in an account with an initial deposit of $100, and which earns 10% interest compounded quarterly for 3 years? A. $107. B. $133. C. $134. D. $313.
FV in three years = PV (1 + rquarter )^12 $100 (1.025)^12 = $134.
- How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%? A. $100. B. $105. C. $110. D. $115.
Interest = $1,000 e .1^ - $1, = $1,000 1.1052 - $1, = $1,105.17- $1, = $105.
- What is the discount factor for $1 to be received in 5 years at a discount rate of 8%? A.. B.. C.. D..
Discount factor = 1/(1.08)^5 = 1/1.4693 =.
- Assume the total expense for your current year in college equals $20,000. Approximately how much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount? A. $952. B. $1,600. C. $1,728. D. $3,973.
$20,000 = x (1.08)^21 $20,000 = 5.0338 x $3,973.12 = x
- How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than the normally advertised 5-year period? Your discount rate is 8%. A. $544. B. $681. C. $740. D. $800.
$7,350.30 vs. $6,805. $544.47 difference_._
- What is the present value of the following set of cash flows at an interest rate of 7%: $1,000 today, $2,000 at end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5? A. $9, B. $10, C. $10, D. $11,
PV = $1,000/(1.07)^0 + $2,000/(1.07)^1 = $4,000/(1.07)^3 + $6,000/(1.07)^5 = $1,000 + $1,869.16 + $3,265.19 + $4,277. = $10,412.
- A young professional offers to buy your car with four, equal annual payments of $3,000, beginning 2 years from today. Assuming that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept? A. Yes; present value is $9,510. B. Yes; present value is $11,372. C. No; present value is $8,645. D. No; present value is $7,461.
PV = $3,000[1/.1 - 1/.1(1.1)^4 ]/1. = $3,000(10 - 6.8301)/1. = $3,000 3.1699/1. = $9,509.60/1. = $8,645.
- How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume a 10% interest rate. A. $297. B. $1,486. C. $1,635. D. $2,000.
Difference = $1,000/.10 - $1,000[1/.10 - 1/.10(1.10)^20 ] = $10,000 - $8,513.56 = $1,486.
- A stream of equal cash payments lasting forever is termed: A. an annuity. B. an annuity due. C. an installment plan. D. a perpetuity.
- The present value of a perpetuity can be determined by: A. Multiplying the payment by the interest rate. B. Dividing the interest rate by the payment. C. Multiplying the payment by the number of payments to be made. D. Dividing the payment by the interest rate.
- A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What is its present value? A. $33,333. B. $37,681. C. $38,333. D. $65,217.
- Your car loan requires payments of $200 per month for the first year and payments of $400 per month during the second year. The annual interest rate is 12% and payments begin in one month. What is the present value of this 2-year loan? A. $6,246. B. $6,389. C. $6,428. D. $6,753.
- You're ready to make the last of four equal, annual payments on a $1,000 loan with a 10% interest rate. If the amount of the payment is $315.47, how much of the last payment is interest? A. $28. B. $31. C. $100. D. $315.
- What will be the monthly payment on a home mortgage of $75,000 at 12% interest, to be amortized over 30 years? A. $771. B. $775. C. $1,028. D. $1,034.
- Your real estate agent mentions that homes in your price range require a payment of approximately $1,200 per month over 30 years at 9% interest. What is the size of the mortgage with these terms? A. $128, B. $147, C. $149, D. $393,
- How much must be saved annually, beginning 1 year from now, in order to accumulate $50,000 over the next 10 years, earning 9% annually? A. $3, B. $3, C. $4, D. $4,
- Approximately how much money should be available in a bank account to provide a $2,500 monthly check that will last for 25 years, during which time the account will earn 8% interest with monthly compounding? A. $261,500. B. $323,800. C. $578,700. D. $690,000.
- The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate. By how much would the value change if this was an annuity due? A. An increase of $ B. An increase of $ C. An increase of $ D. Unknown without knowing number of payments
Difference = $614(1.1) - $614 = $
- With $1.5 million in an account expected to earn 8% annually over the retiree's 30 years of life expectancy, what annual annuity can be withdrawn, beginning today? A. $112, B. $120, C. $123, D. $133,
- "Give me $5,000 today and I'll return $20,000 to you in 5 years," offers the investment broker. To the nearest percent, what annual interest rate is being offered? A. 25% B. 29% C. 32% D. 60%
- A car dealer offers payments of $522.59 per month for 48 months on a $25,000 car after making a $4,000 down payment. What is the loan's APR? A. 6% B. 9% C. 11% D. 12%
r = .0075; or 9% annualized rate
- What APR is being earned on a deposit of $5,000 made 10 years ago if the deposit is worth $9,948.94 today? The deposit pays interest semiannually. A. 3.56% B. 6.76% C. 7.00% D. 7.12%
- An interest rate that has been annualized using compound interest is termed the: A. simple interest rate. B. annual percentage rate. C. discounted interest rate. D. effective annual interest rate.
- What is the relationship between an effective annual rate (EAR) and the annual percentage rate (APR)? A. The APR is lower than the EAR. B. The APR is higher than the EAR. C. The APR can be lower or higher than the EAR. D. The answer depends on the interest rate.
- What is the APR on a loan that charges interest at the rate of 1.4% per month? A. 10.20% B. 14.00% C. 16.80% D. 18.16%
1.4% monthly 12 = 16.8% APR
- If interest is paid m times per year, then the per-period interest rate equals the: A. effective annual rate divided by m. B. compound interest rate times m. C. effective annual rate. D. annual percentage rate divided by m.
- An annual percentage rate will be equal to an effective annual rate if: A. compounding occurs monthly. B. compounding occurs continuously. C. compounding occurs annually. D. an error has occurred; these terms cannot be equal.
- Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold. If inflation averaged 4% annually during the period, how would you describe his purchasing power, on average? A. His purchasing power remained the same. B. His purchasing power decreased by 1% annually. C. He beat inflation by slightly below 2% annually. D. He beat inflation by 5% annually.
10 = 1(1 + r)^40 , r = 5.925% annual nominal interest rate.
- Which of the following statements best describes the real interest rate? A. Real interest rates exceed inflation rates. B. Real interest rates can decline only to zero. C. Real interest rates can be negative, zero, or positive. D. Real interest rates traditionally exceed nominal rates.
- What is the real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually? A. 5.00% B. 5.66% C. 6.00% D. 9.46%
1 + real interest rate = (1 + nominal interest rate)/(1 + inflation) 1 + real interest rate = 1.12/1. Real interest rate = 5.66%.
- What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms and inflation is in existence? A. The real cost is constant. B. The real cost is increasing. C. The real cost is decreasing. D. The price index must be known to answer this question.
