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APPENDIX B
PRESENT AND FUTURE VALUES IN ACCOUNTING
Present Value of 1
Period
s
3% 4% 5% 6% 7% 8% 9% 10% 12%
3 0.915
1
0.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7118
4 0.888
5
0.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6355
5 0.862
6
0.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5674
6 0.837
5
0.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5066
7 0.813
1
0.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4523
8 0.789
4
0.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4039
9 0.766
4
0.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3606
10 0.744
1
0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3220
Future Value of 1
Period
s
3% 4% 5% 6% 7% 8% 9% 10% 12%
3 1.092
7
1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049
4 1.125
5
1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735
5 1.159
3
1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623
6 1.194
1
1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738
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McGraw-Hill Education.
B-1
7 1.229
9
1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107
8 1.266
8
1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760
9 1.304
8
1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731
10 1.343
9
1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058
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McGraw-Hill Education.
B-2
Present Value of an Annuity of 1
Period
s
3% 4% 5% 6% 7% 8% 9% 10% 12%
3 2.828
6
2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018
4 3.717
1
3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373
5 4.579
7
4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048
6 5.417
2
5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114
7 6.230
3
6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638
8 7.019
7
6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676
9 7.786
1
7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7950 5.3282
10 8.530
2
8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502
Future Value of an Annuity of 1
Period
s
3% 4% 5% 6% 7% 8% 9% 10% 12%
3 3.090
9
3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744
4 4.183
6
4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793
5 5.309
1
5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528
6 6.468
4
6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152
7 7.662
5
7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.089
8 8.892
3
9.2142 9.5491 9.8975 10.260 10.637 11.029 11.436 12.300
Copyright © 2016 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
B-3
9 10.15
9
10.583 11.027 11.491 11.978 12.488 13.021 13.580 14.776
10 11.46
4
12.006 12.578 13.181 13.816 14.487 15.193 15.937 17.549
Copyright © 2016 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of
McGraw-Hill Education.
B-4
True / False Questions
1. Interest is the borrower’s payment to the owner of an asset for its use.
2. From the perspective of an account holder, a savings account is a liability with interest.
3. An interest rate is also called a discount rate.
4. Present and future value computations enable companies to measure or estimate the interest
component of holding assets or liabilities over time.
5. The number of periods in a present value calculation may only be expressed in years.
6. The present value factor for determining the present value of $6,300 to be received three
years from today at 10% interest compounded semiannually is 0.7462.
7. The present value of 1 formula is often useful when a borrowed asset must be repaid in full
at a later date and the borrower wants to know the worth of the asset at the future date.
8. In a present value or future value table, the length of one time period may be interpreted as
one year, one month, or any other length of time.
9. The present value of $2,000 to be received nine years from today at 8% interest
compounded annually is $1,000.
10. Sandra has a savings account that has accumulated to $50,000. She started with $28,225,
and earned interest at 10% compounded annually. It took her five years to accumulate the
$50,000.
11. Future value can be found if the interest rate (i), the number of periods (n), and the present
value (p) are known.
12. The number of periods in a future value calculation may only be expressed in years.
13. The future value of $100 compounded semiannually for 3 years at 12% equals $140.49.
14. At an annual interest rate of 8% compounded annually, $5,300 will accumulate to a total
of $7,210.65 in 5 years.
15. An annuity is a series of equal payments occurring at equal intervals.
16. The present value of an annuity table can be used to determine the value today of a series
of payments to be received in the future.
17. A series of equal payments made or received at the end of each period is an ordinary
annuity.
18. The present value of $5,000 per year for three years at 12% compounded annually is
$12,009.
19. With deposits of $5,000 at the end of each year, you will have accumulated $38,578 at the
end of the sixth year if the annual rate of interest is 10%.
20. The future value of an ordinary annuity is the accumulated value of each annuity payment
excluding interest as of the date of the final payment.
21. Interest may be defined as:
A. Time.
B. A borrower’s payment to the owner of an asset for its use.
C. The future value of a present amount.
D. Always a liability.
E. Always an asset.
22. If we want to know the value of present-day assets at a future date, we can use:
A. Present value computations
B. Annuity computations
C. Interest computations.
D. Future value computations.
E. Earnings computations.
23. Which interest rate column would you use from a present value or future value table for
8% interest compounded quarterly?
A. 12%
B. 6%
C. 3%
D. 2%
E. 1%
24. A company is considering investing in a project that is expected to return $350,000 four
years from now. How much is the company willing to pay for this investment if the company
requires a 12% return?
A. $ 55,606
B. $137,681
C. $222,425
D. $265,764
E. $350,000
25. Jason has a loan that requires a single payment of $4,000 at the end of 3 years. The loan’s
interest rate is 6%, compounded semiannually. How much did Jason borrow?
A. $3,358.40
B. $4,000.00
C. $3,660.40
D. $4,776.40
E. $3,350.00
26. Patricia wants to invest a sum of money today that will yield $10,000 at the end of 6
years. Assuming she can earn an interest rate of 6% compounded annually, how much must
she invest today?
A. $7,050
B. $9,400
C. $6,000
D. $8,836
E. $8,306
27. Marshall has received an inheritance and wants to invest a sum of money today that will
yield $5,000 at the end of each of the next 10 years. Assuming he can earn an interest rate of
5% compounded annually, how much of his inheritance must he invest today?
A. $50,000.00
B. $47,500.00
C. $45,125.00
D. $38,608.50
E. $100,000.00
28. Cody invests $1,800 per year from his summer wages at a 4% annual interest rate. He
plans to take a European vacation at the end of 4 years when he graduates from college. How
much will he have available to spend on his vacation?
A. $7,787.52
B. $7,488.00
C. $6,912.00
D. $7,200.00
E. $7,643.70
29. Jessica received a gift of $7,500 at the time of her high school graduation. She invests it
in an account that yields 10% compounded semi-annually. What will the value of Jessica’s
investment be at the end of 5 years?
A. $8,250.00
B. $11,250.00
C. $12,216.75
D. $9,375.00
E. $10,500.00
30. A company expects to invest $5,000 today at 12% annual interest and plans to receive
$15,529 at the end of the investment period. How many years will elapse before the company
accumulates the $15,529?
A. 0.322 years
B. 3.1058 years
C. 5 years
D. 8 years
E. 10 years
31. Keisha has $3,500 now and plans on investing it in a fund that will pay her 12% interest
compounded quarterly. How much will Keisha have accumulated after 2 years?
A. $4,433.80
B. $4,340.00
C. $4,390.40
D. $3,920.00
E. $3,500.00
32. How long will it take an investment of $25,000 at 6% compounded annually to
accumulate to a total of $35,462.50?
A. 4 years
B. 5 years
C. 6 years
D. 2 years
E. 10 years
33. What interest rate is required to accumulate $6,802.50 in four years from an investment of
$5,000?
A. 5%
B. 8%
C. 10%
D. 12%
E. 15%
34. Russell Company has acquired a building with a loan that requires payments of $20,000
every six months for 5 years. The annual interest rate on the loan is 12%. What is the present
value of the building?
A. $ 72,096
B. $113,004
C. $147,202
D. $ 86,590
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B-24
E. $200,000
35. Marc Lewis expects an investment of $25,000 to return $6,595 annually. His investment is
earning 10% per year. How many annual payments will he receive?
A. Five payments
B. Six payments
C. Four payments
D. Three payments
E. More than six payments
36. A company is considering an investment that will return $22,000 semiannually at the end
of each semiannual period for 4 years. If the company requires an annual return of 10%, what
is the maximum amount it is willing to pay for this investment?
A. Not more than $69,738
B. Not more than $139,476
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McGraw-Hill Education.
B-25
C. Not more than $ 88,000
D. Not more than $142,190
E. Not more than $176,000
37. What amount can you borrow if you make six quarterly payments of $4,000 at a 12 %
annual rate of interest?
A. $24,838.00
B. $21,668.80
C. $31,049.00
D. $40,000.00
E. $44,800.00
38. What amount can you borrow if you make seven semiannual payments of $4,000 at an 8%
annual rate of interest?
A. $28,000.00
B. $25,760.00
C. $31,049.00
D. $24,008.40
E. $35,691.20
39. An individual is planning to set-up an education fund for her daughter. She plans to invest
$7,000 annually at the end of each year. She expects to withdraw money from the fund at the
end of 9 years and expects to earn an annual return of 8%. What will be the total value of the
fund at the end of 9 years?
A. $ 87,416
B. $ 68,040
C. $50,400
D. $126,000
E. $45,360
40. An individual is planning to set-up an education fund for his grandchildren. He plans to
invest $10,000 annually at the end of each year. He expects to withdraw money from the fund
at the end of 10 years and expects to earn an annual return of 8%. What will be the total value
of the fund at the end of 10 years?
A. $ 46,320
B. $ 67,107
C. $100,000
D. $144,870
E. $215,890
41. Clara is setting up a retirement fund, and she plans on depositing $5,000 per year in an
investment that will pay 7% annual interest. How long will it take her to reach her retirement
goal of $69,080?
A. 13.816 years
B. 0.072 years
C. 10 years
D. 20 years
E. 5 years
42. The Masterson family is setting up a vacation fund, and they plan on depositing $1,000
per quarter in an investment that will pay 12% annual interest. What amount will they have
available for their vacation at the end of 2 years?
A. $8,000.00
B. $8,960.00
C. $8,892.30
D. $8,240.00
E. $8,487.20
43. A company needs to have $150,000 in 5 years, and will create a fund to insure that the
$150,000 will be available. If it can earn a 6% return compounded annually, how much must
the company invest in the fund today to equal the $150,000 at the end of 5 years?
A. $141,000
B. $112,095
C. $100,000
D. $45,000
E. $105,000
44. Jackson has a loan that requires a $17,000 lump sum payment at the end of four years.
The interest rate on the loan is 5%, compounded annually. How much did Jackson borrow
today?
A. $16,150
B. $13,600
C. $11,504
D. $13,986
E. $15,343
45. A company has $46,000 today to invest in a fund that will earn 4% compounded annually.
How much will the fund contain at the end of 6 years?
A. $58,204
B. $47,840
C. $58,075
D. $57,040
E. $62,582
46. Define interest.
47. Explain the concept of the present value of a single amount.
48. Explain the concept of the future value of a single amount.
49. Explain the concept of the present value of an annuity.
50. Explain the concept of the future value of an annuity.
51. A company needs to have $200,000 in 4 years, and will create a fund to insure that the
$200,000 will be available. If it can earn a 7% return compounded annually, how much must
the company invest in the fund today to equal the $200,000 at the end of 4 years?
52. A company needs to have $150,000 in 5 years, and will create a fund to insure that the
$150,000 will be available. If it can earn a 6% return compounded annually, how much must
the company invest in the fund today to equal the $150,000 at the end of 5 years?
53. Kelsey has a loan that requires a $25,000 lump sum payment at the end of three years.
The interest rate on the loan is 5%, compounded annually. How much did Kelsey borrow
today?
54. Jackson has a loan that requires a $17,000 lump sum payment at the end of four years.
The interest rate on the loan is 5%, compounded annually. How much did Jackson borrow
today?
55. Mason Company has acquired a machine from a dealer that requires a payment of $45,000
at the end of five years. This transaction includes interest at 8%, compounded semiannually.
What is the value of the machine today?
56. Protocol Company has acquired equipment from a dealer that requires equal payments of
$12,000 at the end of the next five years. This transaction includes interest at 9%,
compounded annually. What is the value of the machine today?
57. A company is creating a fund today by depositing $65,763. The fund will grow to
$90,000 after 8 years. What annual interest rate is the company earning on the fund?
58. A company is setting aside $21,354 today, and wishes to have $30,000 at the end of three
years for a down payment on a piece of property. What interest rate must the company earn?
59. A company has $50,000 today to invest in a fund that will earn 7%. How much will the
fund contain at the end of 8 years?
60. A company has $46,000 today to invest in a fund that will earn 4% compounded annually.
How much will the fund contain at the end of 6 years?
61. Trey has $105,000 now. He has a loan of $175,000 that he must pay at the end of 5 years.
He can invest his $105,000 at 10% interest compounded semiannually. Will Trey have
enough to pay his loan at the end of the 5 years?
62. Garcia Brass Fixtures is planning on replacing one of its machines in five years by
making a one-time deposit of $20,000 today and four yearly contributions of $5,000
beginning at the end of year 1. The deposits will earn 10% interest. How much money will
Garcia have accumulated at the end of five years to replace the machine?
63. A company borrows money from the bank by promising to make 6 annual year-end
payments of $27,000 each. How much is the company able to borrow if the interest rate is
9%?
64. A company borrows money from the bank by promising to make 8 semiannual payments
of $9,000 each. How much is the company able to borrow if the interest rate is 10%
compounded semiannually?
65. When you reach retirement age, you will have one fund of $100,000 from which you are
going to make annual withdrawals of $14,702. The fund will earn 6% per year. For how
many years will you be able to draw an even amount of $14,702?
66. City Peewee League borrowed $883,212, and must make annual year-end payments of
$120,000 each. If City’s interest rate is 6%, how many years will it take to pay off the loan?
67. Giuliani Co. lends $524,210 to Craig Corporation. The terms of the loan require that
Craig make six semiannual period-end payments of $100,000 each. What semiannual interest
rate is Craig paying on the loan?
68. A company is beginning a savings plan. It will be saving $15,000 per year for the next 10
years. How much will the company have accumulated after the tenth year-end deposit,
assuming the fund earns 10% interest?
69. A company is beginning a savings plan to purchase a new building. It will be saving
$43,000 per year for the next 10 years. How much will the company have accumulated after
the tenth year-end deposit, assuming the fund earns 9% interest?
70. You are little late planning your retirement, but are looking forward to retiring in 10 years.
You expect to save $6,000 a year at an annual rate of 8%. How much will you have
accumulated when you retire?
71. A company is setting up a sinking fund to pay off $8,654,000 in bonds that are due in 7
years. The fund will earn 7% interest, and the company intends to put away a series of equal
year-end amounts for 7 years. What is the amount of the annual deposits that the company
must make?
72. _____________ is a borrower’s payment to the owner of an asset for its use.
73. The interest rate is also called the __________________ rate.
74. To calculate present value of an amount, two factors are required: The
__________________ and the___________________.
75. An _____________ is a series of equal payments occurring at equal intervals.
76. The future value of an ________________ annuity is the accumulated value of each
annuity payment with interest as of the date of the final payment.
