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Appendix B
Time Value of Money
QUICK STUDIES
Quick Study B-1 (10 minutes)
1.
2%
2.
12%
3.
3%
4.
1%
Quick Study B-2 (10 minutes)
Quick Study B-3 (10 minutes)
In Table B.1, where i = 6% and p = $6,651/$10,000 = 0.6651, the n = 7.
Quick Study B-4 (10 minutes)
In Table B.1, where n = 5 and i = 9%, the p = 0.6499.
Quick Study B-5 (10 minutes)
In Table B.2, where n = 10 and i = 12%, the f = 3.1058.
Quick Study B-6 (10 minutes)
In Table B.3, where n = 6 and i = 7%, the p = 4.7665.
Quick Study B-7 (10 minutes)
EXERCISES
Exercise B-1 (10 minutes)
Exercise B-2 (10 minutes)
Exercise B-3 (10 minutes)
In Table B.3, where n = 8 and p = $57,466/$10,000 = 5.7466, the i = 8%
(investor must earn 8% interest to achieve investment goal).
Exercise B-4 (10 minutes)
Exercise B-5 (10 minutes)
Exercise B-6 (10 minutes)
Exercise B-7 (10 minutes)
Interest rate per period = 12% annual / 12 months per year = 1% per month
Using Table B.3, where n = 40 and i = 1%, the p = 32.8347. This means:
Loan balance ............
$16,417.35
(present value of loan = 32.8347 x $500)
Down payment ..........
6,500.00
(cash)
Total cost ..................
$22,917.35
Exercise B-8 (15 minutes)
Semiannual interest payment = $500,000 x 10% x 1/2 = $25,000
Using Table B.1, where n = 30 and i = 4%, the p = 0.3083 (Principal payment)
Exercise B-11 (15 minutes)
Amount borrowed =
present value of $20,000 at 10% for 3 years
=
$20,000 x 0.7513 (using Table B.1, i = 10%, n = 3)
=
$15,026
Exercise B-12 (10 minutes)
b. p = present value of $15,000 at 8% for 2 years
p = $15,000 x 0.8573
p = $12,859.50
c. There are at least two ways to solve this problem. (1) We can take the
$463 today, compute its future value, and then compare it to the future
value amount of $1,000. (2) We can discount the $1,000 back to the
present and compare it to the $463 today.
d. f = future value of $90 at 5% for 8 years
f = $132.98
e. f = future value of $158,500 at 10% for 8 years
Exercise B-12 (concluded)
f. There are two aspects to this problem: a present value of a lump sum
part and a present value of an annuity part.
Part 1: p = present value of $10,000 at 6% for 10 years
p = $10,000 x 0.5584
p = $5,584
g. p = present value of $500,000 at 6% for 20 years
Exercise B-13 (25 minutes)
1.
First Annuity
Future
Payment
Number of
Periods
Interest
Rate
Table B.1
Value
Amount
Borrowed
First payment ........
$5,000
1
6%
0.9434
$ 4,717
Second payment ...
5,000
2
6
0.8900
4,450
Third payment .......
5,000
3
6
0.8396
4,198
Fourth payment ....
5,000
4
6
0.7921
3,961
Fifth payment ........
5,000
5
6
0.7473
3,737
Sixth payment .......
5,000
6
6
0.7050
3,525
Total borrowed .....
$24,588
Second Annuity
Future
Payment
Number of
Periods
Interest
Rate
Table B.1
Value
Amount
Borrowed
First payment ........
$7,500
1
6%
0.9434
$ 7,076
Second payment ...
7,500
2
6
0.8900
6,675
Third payment .......
7,500
3
6
0.8396
6,297
Fourth payment ....
7,500
4
6
0.7921
5,941
Total borrowed .....
$25,989
Exercise B-13 (Continued)
2.
First Annuity
Payment size .......................................
$ 5,000
Number of payments ..........................
6
Interest rate .........................................
6%
Value from Table B.3 ..........................
4.9173
Present value of the annuity .............
$24,587
(difference from part (1) due to rounding)
Second Annuity
Payment size .......................................
$ 7,500
Number of payments ..........................
4
Interest rate .........................................
6%
Value from Table B.3 ..........................
3.4651
Present value of the annuity .............
$25,988
(difference from part (1) due to rounding)
Exercise B-14 (30 minutes)
1. Present value of the annuity
Payment size .......................................
$13,000
Number of payments ..........................
4
Interest rate .........................................
4%
(semiannual)
Value from Table B.3 ..........................
3.6299
Present value of the annuity .............
$47,189
2. Present value of the annuity
Payment size .......................................
$13,000
Number of payments ..........................
4
Interest rate .........................................
6%
(semiannual)
Value from Table B.3 ..........................
3.4651
Present value of the annuity .............
$45,046
3. Present value of the annuity
Payment size .......................................
$13,000
Number of payments ..........................
4
Interest rate .........................................
8%
(semiannual)
Value from Table B.3 ..........................
3.3121
Present value of the annuity .............
$43,057
Exercise B-15 (15 minutes)
10 years x 4 quarters = 40 interest periods
8% annual / 4 quarters per year = 2% per quarter
Exercise B-16 (15 minutes)
12% annual / 12 months per year = 1% per month
Exercise B-17 (15 minutes)
10 years x 4 quarters per year = 40 total quarters
12% annual / 4 quarters per year = 3% per quarter
Exercise B-19 (20 minutes)
a. (1) Present Value of a single amount.
(3) Use Table B.1, periods = 8 and interest rate = 4%.
OR
(1) Future Value of a single amount.
b. (1) Future Value of an Annuity.
OR
(1) Present Value of an Annuity.
c. (1) Future Value of an Annuity.
d. (1) Present Value of an Annuity.
(2) Multiply $30,000 by p from Table B.3.
