Appendix B
Applying Present and Future Values
QUICK STUDIES
Quick Study B-1 (10 minutes)
Quick Study B-2 (10 minutes)
Quick Study B-3 (10 minutes)
Quick Study B-4 (10 minutes)
Quick Study B-5 (10 minutes)
Quick Study B-6 (10 minutes)
Quick Study B-7 (10 minutes)
EXERCISES
Exercise B-1 (15 minutes)
Exercise B-2 (15 minutes)
Exercise B-3 (10 minutes)
Exercise B-4 (10 minutes)
Exercise B-5 (15 minutes)
10 years x 4 quarters = 40 interest periods
Exercise B-6 (15 minutes)
Exercise B-7 (10 minutes)
Exercise B-8 (10 minutes)
Exercise B-9 (10 minutes)
Interest rate per period = 12% annual / 12 months per year = 1% per month
Exercise B-10 (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
Third payment …….
3
0.8396
Fourth payment ….
4
0.7921
Fifth payment ……..
5
0.7473
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 …
2
0.8900
Fourth payment ….
4
0.7921
2.
First Annuity
Payment size …………………………………
$ 5,000
Number of payments ……………………..
Interest rate …………………………………..
Present value of the annuity ………….
$24,587
Second Annuity
Payment size …………………………………
$ 7,500
Interest rate …………………………………..
Present value of the annuity ………….
$25,988
Exercise B-11 (30 minutes)
1. Present value of the annuity
Payment size …………………………………
$13,000
Number of payments ……………………..
Interest rate …………………………………..
Value from Table B.3 ……………………..
Present value of the annuity ………….
$47,189
2. Present value of the annuity
Payment size …………………………………
$13,000
Number of payments ……………………..
Interest rate …………………………………..
Value from Table B.3 ……………………..
Present value of the annuity ………….
$45,046
3. Present value of the annuity
Payment size …………………………………
$13,000
Number of payments ……………………..
Interest rate …………………………………..
Value from Table B.3 ……………………..
Present value of the annuity ………….
$43,057
0.3083 x $500,000 =
17.2920 x $ 25,000 =
Exercise B-12 (15 minutes)
Exercise B-13 (15 minutes)
Exercise B-14 (10 minutes)
Exercise B-15 (10 minutes)
Exercise B-16 (15 minutes)
Exercise B-17 (15 minutes)
Exercise B-18 (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
d. f = future value of $90 at 5% for 8 years
e. f = future value of $158,500 at 10% for 8 years
Exercise B-18 (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-19 (20 minutes)
OR
b. (1) Future Value of an Annuity.
OR
c. (1) Future Value of an Annuity.