Quiz 2 valuation m7 answer

Appendix B: The Time Value of Money: Future Amounts and Present
Values Answer Key

Multiple Choice Questions

1. If you invested $10,000 at 6% on your 20th birthday how much would you have on
your 40th birthday?
A. $32,071.40
B. $31,180.00
C. $36,785.59
D. $12,158.12
$10,000 × 3.20714 = $32,071.40

AACSB: Analytic
AICPA BB: Critical Thinking
AICPA FN: Measurement
Learning Objective: 4

2. If I invest $20,000 at 2.5% today, how long will it take to reach a minimum of $50,000
compounded semi-annually?
A. 5 years
B. 19 years
C. 9 and ½ years
D. 17 years
[$50,000/$20,000 = 2.5. On Future Value of $1 Table, 2.556 corresponds with 2.5%
interest for 38 periods.] $20,000 × 2.55568 = $51,114 or 38 periods /2 = 19 years

AACSB: Analytic

3. If I invest $50,000 today for 5 years and it grows to $84,253 what rate of interest have
I received?
A. 5%
B. 6%
C. 11%
D. 12%
$50,000 × 1.68506 = $84,253 [$84,253/$50,000 = 1.685. On Future Value of $1 Table,
1.685 corresponds with 5 periods at 11% interest.]

AACSB: Analytic

4. How much must I invest today in order to have $25,000 in 5 years assuming 12%
interest compounded annually?
A. $14,185.75
B. $15,888.00
C. $18,681.50
D. $17.624.00
$25,000 × .56743 = $14,185.75

AACSB: Analytic
AICPA BB: Resource Management

5. Your wealthy aunt wishes to give you a trip to Paris when you graduate from college in
three years. She estimates the trip will cost $4,000. How much must she invest now at 4%
to accumulate enough for you to take this trip?
A. $3,287.72
B. $3,556.00
C. $4,499.44
D. $3,161.24
$4,000 × .88900 = $3,556.00

AACSB: Analytic

6. A scholarship fund has $75,000 to invest now to provide scholarships to high school
students. They want to have at least $150,000 in 8 years. What rate of interest must they
invest this money at to reach their goal?
A. 8%
B. 9%
C. 10%
D. 11%
$75,000/$150,000 = .50. On the Present Value of $1 Table, .50 corresponds to 8 years at
9%.

AACSB: Analytic

7. If I invest $100 at the end of each year for four years at 6% how much will I have at
the end of the fourth year?
A. $421.24
B. $437.46
C. $563.71
D. $432.95
$100 × 4.37462 = $437.46

AACSB: Analytic

8. The difference between the present value and the future value of a sum of money
depends upon:
A. The rate of interest
B. The length of time
C. Both A and B
D. Neither A nor B

AACSB: Reflective Thinking

9. The future value of an annuity is:
A. Always more than the present value
B. Always less than the present value
C. Equal to the present value.
D. Double the present value.


10. The present value of an investment is
A. The amount an investor would pay today to receive a certain amount in the future.
B. The amount an investor would pay today plus the interest the investor would expect to
receive a certain amount in the future.
C. The amount an investor would pay today less the interest the investor requires.
D. 90% of the future value of an investment.


11. Judy Bright has just won the lottery. She can elect to receive her winnings in equal
payments of $200,000 a year for the next ten years on December 31 or to receive
$2,000,000 immediately. If the current interest rate is 6%, which choice will provide the
highest amount:
A. Receiving $2,000,000 immediately.
B. Taking equal payments for 10 years
C. It does not matter since either choice provides the same amount.
D. Refusing to accept the winnings since it is not enough.
$200,000 × 7.36009 = $1,472,018 < $2,000,000

AACSB: Analytic

12. To determine the present value of a single amount to be received or paid at a future
time you need to know all of the following except:
A. The interest rate or discount rate.
B. The number of periods.
C. The future value.
D. The time between periods.


13. To determine the amount to be deposited in a bank today to grow to $5,000 three
years from now at 7% which table should be used?
A. Present value of 1.
B. Future value of 1.
C. Present value of an annuity.
D. No table is required, just multiply $5,000 by 1.07.


14. Anthony Driver wants to buy a new car in 4 years. He knows that he can earn 6%
interest compounded semi-annually. How much must he deposit now in order to have
$26,000 at the end of 4 years?
A. $21,390.20
B. $20,524.66
C. $38,413.96
D. $31.603.26
$26,000 × .78941 = $20,524.66

AACSB: Analytic

15. Compound interest:
A. Is interest only on the principal amount for several years.
B. Is interest on the principal and previously earned interest.
C. Is interest only on previous interest excluding the principal.
D. Is equal to simple interest received for several years.


16. Financial instruments include:
A. Contracts that call for receipts or payment of cash.
B. Equity investment in another business.
C. Cash.
D. All of the above.


17. Financial instruments are recorded at:
A. Future values.
B. Present values plus interest.
C. Present values less interest.
D. Present values.


18. A note that does not include an interest rate should be recorded at:
A. Its face amount if the difference between face and present value is material.
B. Its present value if the difference between face and present value is material.
C. Its face amount at all times
D. Its present value at all times.


19. Joe Notsosmart invested $10,000 at 8% simple interest for 5 years. How much more
would he have received if he had received compound interest annually at the same rate?
A. $4,000
B. $4,693
C. $693
D. $400
Simple interest = ($10,000 × .08 × 5) + $10,000 = $14,000
Compound interest = $10,000 × 1.46933 = $14,693(rounded) or $693 more.

AACSB: Analytic

20. The present value of a cash amount:
A. Is always less than the future value.
B. Is always more than the future value.
C. Is the same as the future value.
D. None of the above.


21. If you receive $20,000 as a gift and invest it at 12% compounded quarterly, how
much will you have at the end of three years?
A. $32,020.60
B. $28,515.20
C. $22,497.20
D. $14,027.60
$20,000 × 1.42576 = $28,515.20

AACSB: Analytic

22. The time value of money is based on the idea that:
A. The value of money in the future equals the interest received in the present.
B. The value of money in the future will be greater than an amount available today.
C. The value of money at present over some length of time will be reduced by inflation.
D. The future value of money will become the current value as time passes.


23. Belle invests $200 at the end of each year in a savings account which pays 5%
annually. How much will Belle have at the end of 5 years?
A. $1,000
B. $1,105.13
C. $1,077.50
D. $1,082.37
$200 × 5.52563 = $1,105.13

AACSB: Analytic

True / False Questions

24. Future value is the amount that must be invested today at a specific interest rate to
receive a particular amount at some future date.
FALSE


25. The present value of an ordinary annuity is the amount that equal payments made at
the end of successive equal periods is worth today.
TRUE


26. The future value of an investment gradually increases toward the present amount.
FALSE


27. Compounding interest assumes the interest on an investment is reinvested.
TRUE


28. Discounting a future amount of a cash receipt will determine the present value of that
receipt.
TRUE


29. The lower the discount rate of an investment, the lower the present value of the
investment.
FALSE

AACSB: Analytic

30. Annuities may provide equal amounts to an investor at fixed periods of time over the
life of an investment.
TRUE


31. The market price of a bond is equal to its present value.
TRUE


32. An annuity due assumes the cash flow will occur at the beginning of the period.
TRUE


33. The rate of interest is usually expressed as an annual rate.
TRUE


34. An interest rate of 12% a year is the same as 6% for 2 months.
FALSE

AACSB: Analytic

35. The obligation for deferred income taxes is the only long-term liability that is not
reported at its present value.
TRUE


36. As the discount rate required by an investor increases, the present value of an
investment decreases.
TRUE

AACSB: Analytic

Essay Questions

37. Use the tables to determine the answers to the following:
(1) How much must be invested now for 5 periods at 6% to amount to $15,000?
(2) How much is $3,000 invested now at 8% in 8 periods worth?
(3) How much is $25,000 compounded quarterly at 12% for 4 years?
(1) $15,000 × .74726 = $11,208.90
(2) $3,000 × 1.85093 = $5,552.79
(3) $25,000 × 1.60471 = $40,117.75

AACSB: Analytic

38. Joan is 75 years old and wishes to retire. She needs to have $48,000 a year plus her
social security to live in the style she is accustomed to. She would like to have enough
money in her retirement account which earns 5% compounded annually to support her for
the next 15 years. How much must be in the fund if she takes the first payment at yearend?
$48,000 × 21.57856 = $1,035,737

AACSB: Analytic

39. Powers Company wishes to issue $2,000,000 of 8%, 10 year bonds which pay interest
semi-annually. The current discount rate is 6%. What amount should the bonds sell for?
$2,000,000 × .55368 = $1,107,360 (PV of future principal payment)
($2,000,000 × .08 × ½) = $80,000 × 14.87747 = $1,190,197 rounded (PV of future
interest payments)
A total of $2,297,557

AACSB: Analytic

40. Sam Rivers has $3,000 to invest. He must decide whether to invest this money for
five years at 10% compounded semi-annually or at 12% compounded annually. Which
option should he select?
$3,000 × 1.62889 = $4,886.67 (10% compounded semi-annually)
$3,000 × 1.76234 = $5,287.02 (12% compounded annually)
He should select 12% compounded annually.

AACSB: Analytic

41. (a) How long will it take Barbara to accumulate $30,000 to buy a car if she invests
$15,000 at 5%? (b) How long will it take if she invests the same amount at 4% semiannually?
(a.) $15,000 × 2.07893 = $31,183.95 (approximately 15 years)
(b.) $15,000 × 1.99989 = $29,998.35 (approximately 17 ½ years)

AACSB: Analytic

Quiz 2 valuation m7 answer

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