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Chapter 6 Time Value of Money Concepts
True/False Questions
1. Compound interest includes interest earned on interest.
2. When interest is compounded, the stated rate of interest exceeds the effective rate of interest.
3. The calculation of future value requires the removal of interest.
4. The company’s credit-adjusted risk-free rate of interest is used when computing present value
applying the expected cash flow approach.
5. The calculation of present value eliminates interest from future cash flows.
6. With an ordinary annuity, a payment is made or received on the date the agreement begins.
7. In the future value of an ordinary annuity, the last cash payment will not earn any interest.
8. An annuity consists of level principal payments plus interest on the unpaid balance.
9. With an annuity due, a payment is made or received on the date the agreement begins.
10. An annuity is a series of equal periodic payments.
11. Given identical current amounts owed and identical interest rates, annual payments of an
ordinary annuity will be greater than annual payments of an annuity due.
12. Other things being equal, the present value of an annuity due will be less than the present
value of an ordinary annuity.
13. A deferred annuity is one in which interest charges are deferred for a stated time period.
14. Monetary assets include only cash and cash equivalents.
Chapter 6 Time Value of Money Concepts
15. Most, but not all, liabilities are monetary liabilities.
Multiple Choice Questions
Use the following to answer questions 16–32:
Present and future value tables of $1 at 3% are presented below:
N
FV $1
PV $1
FVA $1
PVA $1
FVAD $1
PVAD $1
1
1.03000
0.97087
1.0000
0.97087
1.0300
1.00000
2
1.06090
0.94260
2.0300
1.91347
2.0909
1.97087
3
1.09273
0.91514
3.0909
2.82861
3.1836
2.91347
4
1.12551
0.88849
4.1836
3.71710
4.3091
3.82861
5
1.15927
0.86261
5.3091
4.57971
5.4684
4.71710
6
1.19405
0.83748
6.4684
5.41719
6.6625
5.57971
7
1.22987
0.81309
7.6625
6.23028
7.8923
6.41719
8
1.26677
0.78941
8.8923
7.01969
9.1591
7.23028
9
1.30477
0.76642
10.1591
7.78611
10.4639
8.01969
10
1.34392
0.74409
11.4639
8.53020
11.8078
8.78611
11
1.38423
0.72242
12.8078
9.25262
13.1920
9.53020
12
1.42576
0.70138
14.1920
9.95400
14.6178
10.25262
13
1.46853
0.68095
15.6178
10.63496
16.0863
10.95400
14
1.51259
0.66112
17.0863
11.29607
17.5989
11.63496
15
1.55797
0.64186
18.5989
11.93794
19.1569
12.29607
16
1.60471
0.62317
20.1569
12.56110
20.7616
12.93794
16. Today, Thomas deposited $100,000 in a three-year, 12% CD that compounds quarterly. What
is the maturity value of the CD?
a. $109,270.
b. $119,410.
c. $142,576.
d. $309,090.
Chapter 6 Time Value of Money Concepts
17. Carol wants to invest money in a 6% CD account that compounds semiannually. Carol would
like the account to have a balance of $50,000 five years from now. How much must Carol
deposit to accomplish her goal?
a. $35,069.
b. $43,131.
c. $37,220.
d. $35,000.
18. Shane wants to invest money in a 6% CD account that compounds semiannually. Shane would
like the account to have a balance of $100,000 four years from now. How much must Shane
deposit to accomplish his goal?
a. $88,849.
b. $78,941.
c. $25,336.
d. $22,510.
19. Bill wants to give Maria a $500,000 gift in seven years. If money is worth 6% compounded
semiannually, what is Maria's gift worth today?
a. $ 66,110.
b. $ 81,309.
c. $406,545.
d. $330,560.
20. Monica wants to sell her share of an investment to Barney for $50,000 in three years. If money
is worth 6% compounded semiannually, what would Monica accept today?
a. $ 8,375.
b. $41,874.
c. $11,941.
d. $41,000.
21. At the end of the next four years, a new machine is expected to generate net cash flows of
$8,000, $12,000, $10,000, and $15,000, respectively. What are the (rounded) cash flows worth
today if a 3% interest rate properly reflects the time value of money in this situation?
a. $41,556.
b. $39,982.
c. $32,400.
d. $38,100.
22. At the end of each quarter, Patti deposits $500 into an account that pays 12% interest
compounded quarterly. How much will Patti have in the account in three years?
a. $7,096.
b. $7,213.
c. $7,129.
Chapter 6 Time Value of Money Concepts
d. $8,880.
23. Sondra deposits $2,000 in an IRA account on April 15, 2016. Assume the account will earn
3% annually. If she repeats this for the next nine years, how much will she have on deposit on
April 14, 2023?
a. $20,600.
b. $20,928.
c. $23,616.
d. $24,715.
24. Shelley wants to cash in her winning lottery ticket. She can either receive ten $100,000
semiannual payments starting today, or she can receive a lump-sum payment now based on a
6% annual interest rate. What is the equivalent lump-sum payment?
a. $853,020.
b. $801,969.
c. $744,090.
d. $878,611.
Chapter 6 Time Value of Money Concepts
25. On January 1, 2016, you are considering making an investment that will pay three annual
payments of $10,000. The first payment is not expected until December 31, 2018. You are
eager to earn 3%. What is the present value of the investment on January 1, 2016?
a. $26,662.
b. $27,462.
c. $28,286.
d. $29,135.
26. On January 1, 2016, you are considering making an investment that will pay three annual
payments of $10,000. The first payment is not expected until December 31, 2019. You are
eager to earn 3%. What is the present value of the investment on January 1, 2016?
a. $28,286.
b. $25,886.
c. $26,662.
d. $27,300.
27. Rosie's Florist borrows $300,000 to be paid off in six years. The loan payments are
semiannual with the first payment due in six months, and interest is at 6%. What is the amount
of each payment?
a. $25,750.
b. $29,761.
c. $30,139.
d. $25,500.
28. Jimmy has $255,906 accumulated in a 401K plan. The fund is earning a low, but safe, 3% per
year. The withdrawals will take place at the end of each year starting a year from now. How
soon will the fund be exhausted if Jimmy withdraws $30,000 each year?
a. 11 years.
b. 10 years.
c. 8.5 years.
d. 8.8 years.
29. Debbie has $368,882 accumulated in a 401K plan. The fund is earning a low, but safe, 3% per
year. The withdrawals will take place annually starting today. How soon will the fund be
exhausted if Debbie withdraws $30,000 each year?
a. 15 years.
b. 16 years.
c. 14 years.
d. 12.3 years.
30. Jose wants to cash in his winning lottery ticket. He can either receive five $5,000 annual
payments starting today, or he can receive a lump-sum payment now based on a 3% annual
interest rate. What would be the lump-sum payment?
a. $23,586.
b. $22,899.
c. $21,565.
Chapter 6 Time Value of Money Concepts
d. $23,000.
31. Micro Brewery borrows $300,000 to be paid off in three years. The loan payments are
semiannual with the first payment due in six months, and interest is at 6%. What is the amount
of each payment?
a. $ 55,379.
b. $106,059.
c. $ 30,138.
d. $ 60,276.
32. A firm leases equipment under a capital lease (analogous to an installment purchase) that calls
for 12 semiannual payments of $39,014.40. The first payment is due at the inception of the
lease. The annual rate on the lease is 6%. What is the value of the leased asset at inception of
the lease?
a. $388,349.
b. $400,000.
c. $454,128.
d. $440,082.
Chapter 6 Time Value of Money Concepts
Use the following to answer questions 33–38:
Below are excerpts from time value of money tables for the 8% rate.
1
2
3
4
5
6
1
1.000
1.000
0.926
1.080
1.080
0.926
2
1.926
2.080
0.857
2.246
1.166
1.783
3
2.783
3.246
0.793
3.506
1.260
2.577
4
3.577
4.506
0.735
4.867
1.360
3.312
33. Column 1 is an interest table for the:
a. Present value of an ordinary annuity of 1.
b. Future value of an ordinary annuity of 1.
c. Present value of an annuity due of 1.
d. Future value of an annuity due of 1.
34. Column 2 is an interest table for the:
a. Present value of an ordinary annuity of 1.
b. Future value of an ordinary annuity of 1.
c. Present value of an annuity due of 1.
d. Future value of an annuity due of 1.
35. Column 3 is an interest table for the:
a. Present value of 1.
b. Future value of 1.
c. Present value of an ordinary annuity of 1.
d. Present value of an annuity due of 1.
Chapter 6 Time Value of Money Concepts
36. Column 4 is an interest table for the:
a. Present value of an ordinary annuity of 1.
b. Future value of an ordinary annuity of 1.
c. Present value of an annuity due of 1.
d. Future value of an annuity due of 1.
37. Column 5 is an interest table for the:
a. Present value of 1.
b. Future value of 1.
c. Present value of an ordinary annuity of 1.
d. Present value of an annuity due of 1.
38. Column 6 is an interest table for the:
a. Present value of an ordinary annuity of 1.
b. Future value of an ordinary annuity of 1.
c. Present value of an annuity due of 1.
d. Future value of an annuity due of 1.
39. Reba wishes to know how much would be in her savings account if she deposits a given sum
in an account and leaves it there at 6% interest for five years. She should use a table for the:
a. Future value of an ordinary annuity of 1.
Chapter 6 Time Value of Money Concepts
b. Future value of 1.
c. Future value of an annuity of 1.
d. Present value of an annuity due of 1.
Use the following to answer questions 40–44:
Present and future value tables of 1 at 9% are presented below.
PV of $1
FV of
$1
PVA of
$1
FVAD of
$1
FVA of
$1
1
0.91743
1.09000
0.91743
1.0900
1.0000
2
0.84168
1.18810
1.75911
2.2781
2.0900
3
0.77218
1.29503
2.53129
3.5731
3.2781
4
0.70843
1.41158
3.23972
4.9847
4.5731
5
0.64993
1.53862
3.88965
6.5233
5.9847
6
0.59627
1.67710
4.45892
8.2004
7.5233
40. Ajax Company purchased a five-year certificate of deposit for its building fund in the amount
of $220,000. How much should the certificate of deposit be worth at the end of five years if
interest is compounded at an annual rate of 9%?
a. $855,723.
b. $142,985.
c. $319,000.
d. $338,496.
41. How much must be invested now at 9% interest to accumulate to $10,000 in five years?
a. $9,176.
b. $6,499.
c. $5,500.
d. $5,960.
Chapter 6 Time Value of Money Concepts
42. How much must be deposited at the beginning of each year to accumulate to $10,000 in four
years if interest is at 9%?
a. $1,671.
b. $2,570.
c. $2,358.
d. $2,006.
43. Claudine Corporation will deposit $5,000 into a money market sinking fund at the end of each
year for the next five years. How much will accumulate by the end of the fifth and final
payment if the sinking fund earns 9% interest?
a. $32,617.
b. $29,924.
c. $27,250.
d. $26,800.
44. Mustard's Inc. sold the rights to use one of its patented processes that will result in cash
Chapter 6 Time Value of Money Concepts
receipts of $2,500 at the end of each of the next four years and a lump sum receipt of $4,000 at
the end of the fifth year. The total present value of these payments if interest is at 9% is:
a. $10,699.
b. $11,468.
c. $12,100.
d. $14,000.
45. An investment product promises to pay $42,000 at the end of 10 years. If an investor feels this
investment should produce a rate of return of 12%, compounded annually, what’s the most the
investor should be willing to pay for the investment?
a. $ 15,146.
b. $ 13,523.
c. $ 42,000.
d. $130,446.
46. LeAnn wishes to know how much she should invest now at 7% interest in order to accumulate
a sum of $5,000 in four years. She should use a table for the:
a. Present value of 1.
b. Future value of 1.
c. Present value of an ordinary annuity of 1.
d. Future value of an annuity due of 1.
Chapter 6 Time Value of Money Concepts
Use the following to answer questions 47–50:
Present and future value tables of 1 at 11% are presented below.
PV of
FV of
PVA of
FVA of
$1
$1
$1
$1
1
0.90090
1.11000
0.90090
1.0000
2
0.81162
1.23210
1.71252
2.1100
3
0.73119
1.36763
2.44371
3.3421
4
0.65873
1.51807
3.10245
4.7097
5
0.59345
1.68506
3.69590
6.2278
6
0.53464
1.87041
4.23054
7.9129
47. Spielberg Inc. signed a $200,000 noninterest-bearing note due in five years from a production
company eager to do business. Comparable borrowings have carried an 11% interest rate.
What is the value of this debt at its inception?
a. $200,000.
b. $178,000.
c. $118,690.
d. $222,000.
48. On October 1, 2016, Justine Company purchased equipment from Napa Inc. in exchange for a
noninterest-bearing note payable in five equal annual payments of $500,000, beginning Oct 1,
2017. Similar borrowings have carried an 11% interest rate. The equipment would be recorded
at:
a. $2,500,000.
b. $2,225,000.
c. $1,847,950.
d. $2,115,270.
Chapter 6 Time Value of Money Concepts
49. Titanic Corporation leased executive limos under terms of $20,000 down and four equal
annual payments of $30,000 on the anniversary date of the lease. The interest rate implicit in
the lease is 11%. The first year's interest expense would be:
a. $13,200.
b. $10,238.
c. $33,200.
d. $15,543.
50. Polo Publishers purchased a multi-color offset press with terms of $50,000 down and a
noninterest-bearing note requiring payment of $20,000 at the end of each year for five years.
The interest rate implicit in the purchase contract is 11%. Polo would record the asset at:
a. $73,918.
b. $123,918.
c. $130,000.
d. $169,560.
Chapter 6 Time Value of Money Concepts
51. Mary Alice just won the lottery and is trying to decide between the annual cash flow payment
option of $250,000 per year for 25 years beginning today and the lump-sum option. Mary
Alice can earn 6% investing this money. At what lump-sum payment amount would she be
indifferent between the two alternatives?
a. $6,250,000.
b. $3,195,840.
c. $3,637,590.
d. $3,387,590.
52. An investor purchases a 20-year, $1,000 par value bond that pays semiannual interest of $40.
If the semiannual market rate of interest is 5%, what is the current market value of the bond?
a. $ 828.
b. $1,686.
c. $1,000.
d. $ 893.
53. Simpson Mining is obligated to restore leased land to its original condition after its excavation
activities are over in three years. The cash flow possibilities and probabilities for the
restoration costs in three years are as follows:
Cash Outflow Probability
$100,000 40%
150,000 30%
200,000 30%
The company’s credit-adjusted risk-free interest rate is 5%. The liability that Simpson must
Chapter 6 Time Value of Money Concepts
record at the beginning of the project for the restoration costs is:
a. $ 129,576.
b. $ 145,000.
c. $ 125,257.
d. $ 172,768.
54. A series of equal periodic payments that starts more than one period after the agreement is
called:
a. An annuity due.
b. An ordinary annuity.
c. A future annuity.
d. A deferred annuity.
55. A series of equal periodic payments in which the first payment is made one compounding
period after the date of the contract is:
a. A deferred annuity.
b. An ordinary annuity.
c. An annuity due.
d. A delayed annuity.
Chapter 6 Time Value of Money Concepts
56. Loan A has the same original principal, interest rate, and payment amount as Loan B.
However, Loan A is structured as an annuity due, while Loan B is structured as an ordinary
annuity. The maturity date of Loan A will be:
a. Earlier than Loan B.
b. Later than Loan B.
c. The same as Loan B.
d. Indeterminate with respect to loan B.
57. To determine the future value factor for an annuity due for period n when given tables only for
an ordinary annuity:
a. Obtain the FVA factor for n + 1 and deduct 1.
b. Obtain the FVA factor for n and deduct 1.
c. Obtain the FVA factor for n – 1 and add 1.
d. Obtain the FVA factor for n + 1 and add 1.
58. Yamaha Inc. hires a new chief financial officer and promises to pay him a lump-sum bonus
four years after he joins the company. The new CFO insists that the company invest an
amount of money at the beginning of each year in a 7% fixed rate investment fund to insure
the bonus will be available. To determine the amount that must be invested each year, a
computation must be made using the formula for:
a. The future value of a deferred annuity.
b. The future value of an ordinary annuity.
c. The future value of an annuity due.
d. None of these answer choices is correct.
