Appendix A
The Time Value of Money
MULTIPLE CHOICE QUESTIONS
1. Flores Company borrowed $10,000 at 10% interest for 5 years. Which statement is true?
a. Regardless of when the note is repaid, total interest over the loan period is the same.
b. Interest expense is the same regardless of the compounding periods.
c. The amount to be repaid is the same regardless of whether the principal is repaid
$2,000 per year, or as a sum at the end of five years.
d. Interest is less if simple interest is used than if compound interest is used.
2. How much is interest revenue for 90 days on an 8%, 180-day note receivable with a face
value of $25,000?
a. $1,800
b. $500
c. $300
d. $400
3. How much is interest revenue for 30 days on an 8%, 90-day note receivable with a face
value of $6,000?
a. $40
b. $50
c. $90
d. $60
A-2 Test Bank – Appendix – The Time Value of Money
4. The following computation took place:
$20,000 divided by the future value of a 12-year, 4% ordinary annuity
What question will this computation answer?
a. How much must be invested now so that equal payments can be withdrawn at the
end of each year for 12 years?
b. How much must be invested now so that $20,000 is accumulated by the end of the
12th year?
c. How much will be available at the end of the12th year if a payment of $20,000 is
deposted now?
d. How much must be deposited at the end of every year so that $20,000 is available at
the end of 12 years?
5. Interest is compounded annually. What is the total amount of interest on a $7,000 note
payable at the end of five years at 8%?
a. $3,000
b. $3,285
c. $7,000
d. $3,791
e. $7,100
6. Which timing of payments is true for an ordinary annuity?
a. All payments occur at the beginning of the first year.
b. Payments begin immediately and occur once per year on the last day of each year.
c. Payments occur at the end of each period.
d. Payments occur at the beginning of each period.
7. Interest is compounded quarterly on a $10,000 note payable for 1 year at 12%. How
much is total interest on the note?
a. $1,338
b. $1,286
c. $1,255
d. $1,506
Test Bank – Appendix – The Time Value of Money A-3
8. You need to calculate the present value of an amount at 10% compounded quarterly for
2 years. What interest factor will you use?
a. 10% for 4 periods
b. 2.5% for 8 periods
c. 20% for 2 periods
d. 10% for 8 periods
9. Sierra Capital wants to accumulate $100,000 at the end of 10 years to fund retirement
benefits for its accountant. Annual deposits will be made into a special account earning
6%, beginning at the end of year 1. To calculate the amount of the equal deposits, use
the
a. future value of a annuity due.
b. present value of a single amount.
c. future value of an ordinary annuity.
d. present value of an annuity.
10. Malcom Corp. will deposit $10,000 annually at the end of each year for five years.
Malcom will earn 6%. How much will be accumulated at the end of the 5 years?
a. $65,321
b. $70,399
c. $50,000
d. $56,371
11. Calculate the future value of equal semiannual payments of $9,000 at 12% compounded
semiannually for 4 years. The answer is
a. $43,014.
b. $55,888.
c. $89,077.
d. $114,757.
12. Present value is
a. how much today’s money will be worth in the future.
b. the amount of money that must be invested now to produce a known future value.
c. always larger than the future value.
d. the total cost of interest over several years.
A-4 Test Bank – Appendix – The Time Value of Money
13. How much would you deposit today in a savings account that earns 10%, in order that
you can make equal annual withdrawals of $1,200 each at the end of each of the next 15
years?
a. $5,013
b. $9,127
c. $19,800
d. $18,000
e. $38,127
14. Miracle Corporation wants to withdraw $60,000 from a savings account at the end of
each year for ten years beginning one year from now. The savings earns 10% and is
compounded annually. Which one of the following reflects the correct procedure to
determine the required initial investment at the beginning of the first year?
a. $60,000 times the present value of a 10-year, 10% ordinary annuity.
b. $60,000 divided by the future value of a 10-year, 10% ordinary annuity.
c. $60,000 times the future value of a 10-year, 10% ordinary annuity.
d. $6,000 divided by the present value of a 10-year, 10% ordinary annuity.
15. An annuity due and an ordinary annuity have equal payments, the same interest rates,
and the amount of time between the payments is equal. Which statement is true?
a. The present value of the annuity due is less than the present value of the ordinary
annuity.
b. The future value of the annuity due is less than the future value of the ordinary
annuity.
c. The future value of the annuity due is equal to the future value of the ordinary
annuity.
d. The present value of the annuity due is greater than the present value of the ordinary
annuity.
16. An amount is deposited for five years at 6% and is compounded semi-annually. Which
interest rate and periods will be used to determine the present value?
a. 8% for 5 periods
b. 3% for 10 periods
c. 3% for 2.5 periods
d. 8% for 10 periods
Test Bank – Appendix – The Time Value of Money A-5
17. To determine how much must be deposited in the bank today so that you can withdraw 6
annual payments beginning one year from now, which interest factor will you need?
a. Future value of an ordinary annuity of 1
b. Future value of an annuity due of 1
c. Present value of an ordinary annuity of 1
d. Present value of an annuity due of 1
18. This morning Roseland Inc. purchased a land for a new manufacturing facility at a price
of $750,000. However, the seller is financing the transaction and equal quarterly
payments will be made starting today, July 1, 2005. The last semi-annual payment will
be made on December 31, 2024. The applicable interest rate is 8%. How much is each
semi-annual payment?
a. $35,365
b. $36,435
c. $37,893
d. None of the above
19. Carter Holding Co. intends to purchase a new accounting system, including hardware,
software and a complete package of services needed to get the new system up and
running. Carter has for options for paying for the new system. Which of the four options
is the least costly if the applicable interest rate is 12%?
a. Make a lump sum payment of $100,000 today
b. Make 10 annual payments of $16,000, starting today
c. Make 40 quarterly payments of $4,000, starting today
d. Make one lump sum payment of $150,000 four years from today
A-6 Test Bank – Appendix – The Time Value of Money
20. Jim Hall invested $12,000 at 8% annual interest and left the money invested without
withdrawing any of the interest for 15 years. At the end of the 15 years, Jim withdrew
the accumulated amount of money. What amount did Jim withdraw, assuming the
investment earns simple interest?
a. $14,400
b. $26,400
c. $22,500
d. $13,200
21. Karla Simpson Carson invested $12,000 at 8% annual interest and left the money
invested without withdrawing any of the interest for 15 years. At the end of the 15 years,
Karla decided to withdraw the accumulated amount of money. Karla has found the
following values in various tables related to the time value of money.
Present Value of 1 for 15 periods at 8% 0.31524
Future Value of 1 for 15 periods at 8% 3.17217
Present Value of an Annuity of 1 for 15 periods at 8% 8.55948
Future Value of an Annuity of 1 for 15 periods at 8% 27.15211
Which factor would she use to compute the amount she would withdraw, assuming that
the investment earns interest compounded annually?
a. 0.31524
b. 3.17217
c. 8.55948
d. 27.15211
Test Bank – Appendix – The Time Value of Money A-7
22. Thomas Young invested $12,000 at 8% annual interest and left the money invested
without withdrawing any of the interest for 15 years. At the end of the 15 years, Thomas
decided to withdraw the accumulated amount of money. Thomas has found the
following values in various tables related to the time value of money.
Present Value of 1 for 15 periods at 8% 0.31524
Future Value of 1 for 15 periods at 8% 3.17217
Present Value of an Annuity of 1 for 15 periods at 8% 8.55948
Future Value of an Annuity of 1 for 15 periods at 8% 27.15211
To the closest dollar, which amount would he withdraw, assuming that the investment
earns interest compounded annually?
a. $32,583
b. $102,714
c. $15,783
d. $38,066
23. Rowan and Lisa Sharp invested $10,000 in a savings account paying 5% annual interest
when their son, Jeremy, was born. They also deposited $500 on each of his birthdays
until he was 20 (including his 20th birthday). Rowan and Lisa have obtained the following
values related to the time value of money to help them with their planning process for
their compounded interest decisions.
Present Value of 1 for 20 periods at 5% 0.37689
Future Value of 1 for 20 periods at 5% 2.65330
Present Value of an Annuity of 1 for 20 periods at 5% 12.46221
Future Value of an Annuity of 1 for 20 periods at 5% 33.06595
To the closest dollar, how much was in the savings account on his 20th birthday (after
the last deposit)?
a. $53,066
b. $43,066
c. $30,000
d. $26,533
A-8 Test Bank – Appendix – The Time Value of Money
24. Harrison Marshall borrowed $65,000 on June 1, 2009. This amount plus accrued
interest at 8% compounded annually is to be repaid on June 1, 2022. Harrison has
obtained the following values related to the time value of money to help him with his
financing process and compounded interest decisions.
Present Value of 1 for 13 periods at 8% 0.36770
Future Value of 1 for 13 periods at 8% 2.71962
Present Value of an Annuity of 1 for 13 periods at 8% 7.90378
Future Value of an Annuity of 1 for 13 periods at 8% 21.49530
To the closest dollar, how much will Harrison have to repay on June 1, 2022?
a. $132,600
b. $310,707
c. $116,375
d. $176,775
25. Stranton Company is considering investing in an annuity contract that will return $40,000
annually at the end of each year for 12 years. Stranton has obtained the following
values related to the time value of money to help in its planning process and
compounded interest decisions.
Present Value of 1 for 12 periods at 9% 0.35554
Future Value of 1 for 12 periods at 9% 2.81267
Present Value of an Annuity of 1 for 12 periods at 9% 7.16073
Future Value of an Annuity of 1 for 12 periods at 9% 20.14072
To the closest dollar, what amount should Stranton Company pay for this investment if it
earns a 9% return?
a. $497,066
b. $592,507
c. $805,629
d. $286,429
Test Bank – Appendix – The Time Value of Money A-9
26. Morgan Company earns 11% on an investment that pays back $220,000 at the end of
each of the next 5 years. Morgan’s finance department has the following values related
to the time value of money to help in its planning process and compounded interest
decisions.
Present Value of 1 for 5 periods at 11% 0.59345
Future Value of 1 for 5 periods at 11% 1.68506
Present Value of an Annuity of 1 for 5 periods at 11% 3.69590
Future Value of an Annuity of 1 for 5 periods at 11% 6.22780
To the closest dollar, what is the amount Nathan invested to earn the 11% rate of
return?
a. $370,713
b. $130,559
c. $59,525
d. $141,935
27. Everett Corporation issues a 8%, 9-year mortgage note on January 1, 2009, to obtain
financing for new equipment. Land is used as collateral for the note. The terms provide
for semiannual installment payments of $131,600. The following values related to the
time value of money were available to Everett to help them with their planning process
and compounded interest decisions.
Present Value of 1 for 9 periods at 8% 0.50025
Present Value of 1 for 18 periods at 4% 0.49363
Future Value of 1 for 9 periods at 8% 1.99900
Future Value of 1 for 18 periods at 4% 2.02582
Present Value of an Annuity of 1 for 9 periods at 8% 6.24689
Present Value of an Annuity of 1 for 18 periods at 4% 12.65930
Future Value of an Annuity of 1 for 9 periods at 8% 12.48756
Future Value of an Annuity of 1 for 18 periods at 4% 25.64541
To the closest dollar, what were the cash proceeds received from the issuance of the
note?
a. $822,091
b. $947,520
c. $1,665,964
d. $1,643,363
A-10 Test Bank – Appendix – The Time Value of Money
28. Gaynor Company is considering purchasing equipment. The equipment will produce the
following cash flows: Year 1, $25,000; Year 2, $45,000; Year 3, $60,000. Below is some
of the time value of money information that Gaynor has compiled that might help them in
their planning and compounded interest decisions.
Gaynor requires a minimum rate of return of 11%. To the closest dollar, what is the
maximum price Gaynor should pay for the equipment?
a. $317,682
b. $102,917
c. $165,253
d. $246,209
29. Clarkson Corporation earns 12% on an investment that will return $900,000, 7 years
from now. Below is some of the time value of money information that Clarkson has
compiled that might help in planning compounded interest decisions.
Present Value of 1 for 7 periods at 12% 0.45235
Future Value of 1 for 7 periods at 12% 2.21068
Present Value of an Annuity of 1 for 7 periods at 12% 4.56376
Future Value of an Annuity of 1 for 7 periods at 12% 10.08901
To the closest dollar, what is the amount Clarkson should invest now to earn this rate of
return?
a. $198,961
b. $407,115
c. $756,000
d. $410,738
1 period,
11%
2 periods,
11%
3 periods,
11%
Present Value of 1
0.90090
0.81162
0.73119
Future Value of 1
1.11000
1.23210
1.36763
Present Value of an Annuity of 1
0.90090
1.71252
2.44371
Future Value of an Annuity of 1
1.00000
2.12000
3.37440
Test Bank – Appendix – The Time Value of Money A-11
30. Turner Company is considering an investment, which will return a lump sum of $450,000
four years from now. Below is some of the time value of money information that Turner
has compiled that might help in planning compounded interest decisions.
Present Value of 1 for 4 periods at 10% 0.68301
Future Value of 1 for 4 periods at 10% 1.46410
Present Value of an Annuity of 1 for 4 periods at 10% 3.16986
Future Value of an Annuity of 1 for 4 periods at 10% 4.64100
To the closest dollar, what amount should Turner Company pay for this investment to
earn a 10% return?
a. $270,000
b. $180,000
c. $307,355
d. $356,609
31. Mitch has been offered three different contracts for a service he provides.
Contract 1: $9,000 received at the beginning of each year for ten years, compounded
at a 6 percent annual rate.
Contract 2: $9,000 received today and $20,000 received ten years from today. The
relevant interest rate is 12 percent.
Contract 3: $9,000 received at the end of Years 4, 5, and 6. The relevant annual
interest rate is 10 percent.
What is the present value of Contract 1?
a. $66,240.81
b. $118,627.11
c. $70,215.21
d. $125,744.76
Solution: C
Contract 1
Present value = $9,000 Present value factor for an annuity due for i = 6% and n = 10
= $9,000 7.80169 (from Table 6)
= $70,215.21
A-12 Test Bank – Appendix – The Time Value of Money
32. Mitch has been offered three different contracts for a service he provides.
Contract 1: $9,000 received at the beginning of each year for ten years,
compounded at a 6 percent annual rate.
Contract 2: $9,000 received today and $20,000 received ten years from today. The
relevant interest rate is 12 percent.
Contract 3: $9,000 received at the end of Years 4, 5, and 6. The relevant annual
interest rate is 10 percent.
What is the present value of Contract 2?
a. $9,337.13
b. $71,117.00
c. $29,000.00
d. $15,439.40
Solution: D
Contract 2
Present value = $9,000 + ($20,000 Present value factor for i = 12% and n = 10)
= $9,000 + ($20,000 0.32197 from Table 4)
= $15,439.40
33. Mitch has been offered three different contracts for a service he provides.
Contract 1: $9,000 received at the beginning of each year for ten years, compounded
at a 6 percent annual rate.
Contract 2: $9,000 received today and $20,000 received ten years from today. The
relevant interest rate is 12 percent.
Contract 3: $9,000 received at the end of Years 4, 5, and 6. The relevant annual
interest rate is 10 percent.
What is the present value of Contract 3?
a. $18,497.15
b. $16,815.56
c. $24,619.68
d. $22,381.52
Solution: B
Contract 3
Present value = ($9,000 Present value factor for an ordinary annuity for i = 10% and n = 3)
Present value factor for i = 10% and n = 3
= ($9,000 2.48685 from Table 5) 0.75131 from Table 4
= $16,815.56
Test Bank – Appendix – The Time Value of Money A-13
34. Morgan is considering entering into a contract to sell a building on January 1 in
exchange for a note. The note pays a lump sum payment of $300,000 in ten years and
ten annual payments of $2,500 beginning on the date of sale (January 1). If the annual
interest rate is 10 percent, what is the total present value of the contract?
a. $159,489.92
b. $132,559.55
c. $131,023.42
d. $155,505.55
Solution: B
(1) Present value of annual receipts:
Value = $2,500 Present value factor for an annuity due for i = 10% and n = 10
= $2,500 6.75902 (from Table 6) = $16,897.55
(2) Present value of lump-sum receipt:
Value = $300,000 Present value factor for i =10% and n = 10
= $300,000 0.38554 (from Table 4) = $115,662.00
(3) Total present value:
Value = $16,897.55 + $115,662.00 = $132,559.55
35. Kaitlin is contemplating investing in Cocoa Beach Tans. She estimates that the
company will pay the following dividends per share at the end of the next four years and
that the current price of the company’s common stock, which is $100 per share, will
remain unchanged.
Dividends
Year 1
Year 2
Year 3
Year 4
$6
$7
$8
$9
If Kaitlin wants to earn 12 percent on her investment and plans to sell the investment at
the end of the fourth year, how much would she be willing to pay for one share of
common stock? (Round all calculations to the nearest cent.)
a. $130.00
b. $119.07
c. $85.90
d. $82.00
Solution: C
Present value = Present value of dividends + Present value of proceeds
= [($6 0.89286 from Table 4) + ($7 0.79719 from Table 4) + ($8 0.71178
from Table 4) + ($9 0.63552 from Table 4)] + ($100 0.63552 from Table 4)
= $5.36 + $5.58 + $5.69 + $5.72 + $63.55 = $85.90
A-14 Test Bank – Appendix – The Time Value of Money
MATCHING QUESTIONS
1. For each of the following situations in A through D, indicate the abbreviation of the table
that should be used to solve for the solution requested. Place the abbreviation of the
respective table in the space provided. You may use each table more than once or not at
all.
Tables
PVOA Present value of an ordinary annuity
PVAD Present value of an annuity due
PV Present value of a sum
FVOA Future value of an ordinary annuity
FVAD Future value of an annuity due
FV Future value of a sum
_______A. How much would an investor deposit today in order to withdraw $12,000 at the
beginning of each of the next four years, assuming that the first payment is
withdrawn one year from today?
_______B. If interest rates are compounded semi-annually, how much will a company
accumulate in three years after making six equal semi-annual payments of $15,000
each? The first payment will be made today.
_______C. If interest rates are compounded monthly, how much can a company withdraw per
month for 6 months beginning one month from now if $100,000 is deposited today?
_______D. You want to buy a house for $200,000 and finance it with interest compounded
monthly. If it is financed over a 12-year period, what will be the amount of each
annual payment, the first of which will be due at the beginning of the first year?
SHORT PROBLEMS
1. How much must be invested now to receive $10,000 per year for ten years if the first
$10,000 is received today and the rate is 10%?
Solution:
Test Bank – Appendix – The Time Value of Money A-15
2. Ocean Corporation purchased a machine with a cash price of $35,000. Payments will be
made at the end of every quarter for 30 payments beginning at the end of each quarter.
The machine was financed at 12%. How much is each payment?
3. You deposited $4,000 per year annually starting on January 1, 2005 in a bank account
which earns 10%. How much will accumulate by December 31, 2008, the date of the
final payment?
4. Middlesex Enterprises plans to issue $120,000 of 10-year, 6% bonds. The effective yield
at the time of issuance is 8%.
A. How much will the bonds sell for in the market if interest is paid annually?
B. How much will the bonds sell for in the market if interest is paid semi-annually?
A-16 Test Bank – Appendix – The Time Value of Money
5. The phone rings. You answer, “Hello.” Is this Billy Bob?” “Yes, it is.” “This is Ed
McMahon. Congratulations! You have just won the Just Kidding Clearing House
sweepstakes! How would you like us to pay you?”
You ponder over the best choice of accepting your winnings:
1. Equal payments of $250,000 at the end of each year for twenty years
2. A lump-sum payment of $2,400,000 today
3. A lump-sum payment of $100,000 today and payments of $400,000 at the end of
every year for 10 years
All earnings can be invested at 10 percent. Make a choice of one of the three options.
Show calculations.
6. Calculate the purchase price of equipment that requires 20 annual payments of $5,000
at the end of each year, beginning one year after the purchase contract is signed. The
interest rate on the loan is 7%.
SHORT ESSAY QUESTIONS
1. Explain the concept of the “time value of money.”
Solution:
Test Bank – Appendix – The Time Value of Money A-17
2. How does inflation affect the value of money over time?
Solution:
3. How does an annuity due differ from an ordinary annuity?
4. Why is present value not used more liberally on financial statements?