Chapter 3: The Time Value of Money MCQs solved

 Multiple-Choice Quiz

Chapter 3:   The Time Value of Money

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1. You want to buy an ordinary annuity that will pay you $4,000 a year for the next 20 years. You expect annual interest rates will be 8 percent over that time period. The maximum price you would be willing to pay for the annuity is closest to

$32,000.

$39,272.             Correct!

 PVA = $4,000 (PVIFA at 8% for 20 periods)

 PVA = $4,000 (9.818) = $39,272

$40,000.

$80,000.

2. With continuous compounding at 10 percent for 30 years, the future value of an initial investment of $2,000 is closest to

$34,898.

$40,171.           Correct!

 FVA = $2,000 * e^(.10 * 30)

 FVA = $2,000 (20.0855) = $40,171

$164,500.

$328,282.

3. In 3 years you are to receive $5,000. If the interest rate were to suddenly increase, the present value of that future amount to you would

fall.

rise.

remain unchanged.

cannot be determined without more information.

4. Assume that the interest rate is greater than zero. Which of the following cash-inflow streams should you prefer?

    Year1      Year2     Year3      Year4    

$400       $300      $200        $100

$100       $200      $300        $400

$250       $250      $250        $250

Any of the above, since they each sum to $1,000.

5. You are considering investing in a zero-coupon bond that sells for $250. At maturity in 16 years it will be redeemed for $1,000. What approximate annual rate of growth does this represent?

8 percent.

9 percent.                                             Hint

                                                        $250 (FVIF at X% for 16 periods) = $1,000 

                                                               (FVIF at approx. 9% for 16 periods) = $1,000/$250 = 4 

                         OR -- noting that $250 doubles twice over 16 years to yield $1,000 we can use the Rule of 72 as follows: 72/(16/2) = 9 percent

12 percent.

25 percent.

6. To increase a given present value, the discount rate should be adjusted

upward.

downward.

True.

Fred.

7. For $1,000 you can purchase a 5-year ordinary annuity that will pay you a yearly payment of $263.80 for 5 years. The compound annual interest rate implied by this arrangement is closest to

8 percent.

9 percent.

10 percent.           Hint

                                           $1,000 = $263.80 (PVIFA at X% for 5 periods)

                                          $1,000 / $263.80 = (PVIFA at X% for 5 periods)

                                                         3.791 = (PVIFA at 10% for 5 periods)

11 percent.

8. You are considering borrowing $10,000 for 3 years at an annual interest rate of 6%. The loan agreement calls for 3 equal payments, to be paid at the end of each of the next 3 years. (Payments include both principal and interest.) The annual payment that will fully pay off (amortize) the loan is closest to

$2,674.

$2,890.

$3,741.                Correct!

                                        PVA = R (PVIFA at 6% for 3 periods)

                                             $10,000 = R (2.673)

                                       R = $10,000 / 2.673 = $3,741

$4,020.

9. When n = 1, this interest factor equals one for any positive rate of interest.

PVIF

FVIF

PVIFA

FVIFA

None of the above (you can't fool me!)

10. (1 + i)ⁿ

PVIF

FVIF

PVIFA

FVIFA

11. You can use          to roughly estimate how many years a given sum of money must earn at a given compound annual interest rate in order to double that initial amount .

Rule 415

the Rule of 72

the Rule of 78

Rule 144

12. In a typical loan amortization schedule, the dollar amount of interest paid each period          .

increases with each payment

decreases with each payment

remains constant with each payment

13. In a typical loan amortization schedule, the total dollar amount of money paid each period          .

increases with each payment

decreases with each payment

remains constant with each payment