34
57) Explain the concept of the present value of an annuity.
58) Explain the concept of the future value of an annuity.
35
Present Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
0.9151
0.8890
0.8638
0.8396
0.8163
0.7938
0.7722
0.7513
0.7118
4
0.8885
0.8548
0.8227
0.7921
0.7629
0.7350
0.7084
0.6830
0.6355
5
0.8626
0.8219
0.7835
0.7473
0.7130
0.6806
0.6499
0.6209
0.5674
6
0.8375
0.7903
0.7462
0.7050
0.6663
0.6302
0.5963
0.5645
0.5066
7
0.8131
0.7599
0.7107
0.6651
0.6227
0.5835
0.5470
0.5132
0.4523
8
0.7894
0.7307
0.6768
0.6274
0.5820
0.5403
0.5019
0.4665
0.4039
9
0.7664
0.7026
0.6446
0.5919
0.5439
0.5002
0.4604
0.4241
0.3606
10
0.7441
0.6756
0.6139
0.5584
0.5083
0.4632
0.4224
0.3855
0.3220
Future Value of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
1.0927
1.1249
1.1576
1.1910
1.2250
1.2597
1.2950
1.3310
1.4049
4
1.1255
1.1699
1.2155
1.2625
1.3108
1.3605
1.4116
1.4641
1.5735
5
1.1593
1.2167
1.2763
1.3382
1.4026
1.4693
1.5386
1.6105
1.7623
6
1.1941
1.2653
1.3401
1.4185
1.5007
1.5869
1.6771
1.7716
1.9738
7
1.2299
1.3159
1.4071
1.5036
1.6058
1.7138
1.8280
1.9487
2.2107
8
1.2668
1.3686
1.4775
1.5938
1.7182
1.8509
1.9926
2.1436
2.4760
9
1.3048
1.4233
1.5513
1.6895
1.8385
1.9990
2.1719
2.3579
2.7731
10
1.3439
1.4802
1.6289
1.7908
1.9672
2.1589
2.3674
2.5937
3.1058
Present Value of an Annuity of 1
Periods
3%
4%
5%
6%
7%
8%
9%
10%
12%
3
2.8286
2.7751
2.7232
2.6730
2.6243
2.5771
2.5313
2.4869
2.4018
4
3.7171
3.6299
3.5460
3.4651
3.3872
3.3121
3.2397
3.1699
3.0373
5
4.5797
4.4518
4.3295
4.2124
4.1002
3.9927
3.8897
3.7908
3.6048
6
5.4172
5.2421
5.0757
4.9173
4.7665
4.6229
4.4859
4.3553
4.1114
7
6.2303
6.0021
5.7864
5.5824
5.3893
5.2064
5.0330
4.8684
4.5638
8
7.0197
6.7327
6.4632
6.2098
5.9713
5.7466
5.5348
5.3349
4.9676
9
7.7861
7.4353
7.1078
6.8017
6.5152
6.2469
5.9952
5.7950
5.3282
10
8.5302
8.1109
7.7217
7.3601
7.0236
6.7101
6.4177
6.1446
5.6502
Future Value of an Annuity of 1
Periods
3%
4%
5%
6%
8%
9%
10%
12%
3
3.0909
3.1216
3.1525
3.1836
3.2464
3.2781
3.3100
3.3744
4
4.1836
4.2465
4.3101
4.3746
4.5061
4.5731
4.6410
4.7793
5
5.3091
5.4163
5.5256
5.6371
5.8666
5.9847
6.1051
6.3528
6
6.4684
6.6330
6.8019
6.9753
7.3359
7.5233
7.7156
8.1152
7
7.6625
7.8983
8.1420
8.3938
8.9228
9.2004
9.4872
10.0890
8
8.8923
9.2142
9.5491
9.8975
10.6366
11.0285
11.4359
12.2997
9
10.1591
10.5828
11.0266
11.4913
12.4876
13.0210
13.5795
14.7757
10
11.4639
12.0061
12.5779
13.1808
14.4866
15.1929
15.9374
17.5487
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59) 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?
60) 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?
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61) 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?
62) 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?
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63) 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?
64) Protocol Company has acquired equipment from a dealer that requires equal payments of
$12,000 at the end of each of the next five years. This transaction includes interest at 9%,
compounded annually. What is the value of the machine today?
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65) 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?
66) 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?
40
67) 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?
68) 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?
41
69) 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?
70) 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?
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71) 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%?
72) 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?
6.4632 is the PV factor on the Present Value of an Annuity table; n = 8; i = 10%/2 = 5%
Difficulty: 2 Medium
Topic: Present Value of an Annuity
Learning Objective: B-P3 Apply present value concepts to an annuity by using interest tables.
Bloom’s: Understand
AACSB/Accessibility: Analytical Thinking / Keyboard Navigation
AICPA: BB Industry; FN Decision Making
73) 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?
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74) 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?
75) 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?
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76) 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?
77) 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?
78) 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?
79) 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?
80) ________ is a borrower’s payment to the owner of an asset for its use.
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81) The interest rate is also called the ________ rate.
82) To calculate present value of an amount, two factors are required: The ________ and
the________.
83) An ________ is a series of equal payments occurring at equal intervals.
84) The future value of an ________ annuity is the accumulated value of each annuity payment
with interest as of the date of the final payment.