Appendix B
Applying Present and Future Values
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)
Quick Study B-4 (10 minutes)
Quick Study B-5 (10 minutes)
In Table B.2, where n = 10 and i = 12%, the f = 3.1058.
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Quick Study B-6 (10 minutes)
Quick Study B-7 (10 minutes)
EXERCISES
Exercise B-1 (10 minutes)
Exercise B-2 (10 minutes)
Exercise B-3 (10 minutes)
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)
Using Table B.3, where n = 30 and i = 4%, the p = 17.2920 (Interest payments)
0.3083 x $500,000 =
present value of maturity amount
17.2920 x $ 25,000 =
present value of interest payments
cash proceeds
Exercise B-9 (15 minutes)
In Table B.1, where n = 6 and i = 10%, the p = 0.5645.
Exercise B-10 (15 minutes)
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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)
a. p = present value of $60,000 at 9% for 4 years
b. p = present value of $15,000 at 8% for 2 years
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
d. f = future value of $90 at 5% for 8 years
Formula: $90 = f x 0.6768; then solve for f
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
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
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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
2.5 years x 12 months per year = 30 total months
Exercise B-17 (15 minutes)
10 years x 4 quarters per year = 40 total quarters
12% annual / 4 quarters per year = 3% per quarter
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Exercise B-19 (20 minutes)
a. (1) Present Value of a single amount.
(2) Multiply $10,000 by p from Table B.1.
(3) Use Table B.1, periods = 8 and interest rate = 4%.
b. (1) Future Value of an Annuity.
(2) Divide $10,000 by f from Table B.4.
(3) Use Table B.4, periods = 8 and interest rate = 4%.
OR
(3) Use Table B.4, periods = 40 and interest = 8%.