March 26, 2020

Appendix B

Time Value of Money

QUICK STUDIES

Quick Study B-1 (10 minutes)

1.

2%

n = 8 periods

Quick Study B-2 (10 minutes)

In Table B.1, where n = 15 and p = $2,745/$10,000 = 0.2745, the i = 9%.

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)

Quick Study B-5 (10 minutes)

Quick Study B-6 (10 minutes)

Quick Study B-7 (10 minutes)

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

2.

First Annuity

Payment size .......................................

$ 5,000

Number of payments ..........................

6

Interest rate .........................................

6%

Exercise B-11 (30 minutes)

1. Present value of the annuity

Payment size .......................................

$13,000

2. Present value of the annuity

Payment size .......................................

$13,000

3. Present value of the annuity

Payment size .......................................

$13,000

Exercise B-12 (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)

Exercise B-13 (15 minutes)

Exercise B-14 (10 minutes)

Exercise B-15 (10 minutes)

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

In Table B.2, where n = 40 and i = 3%, the f = 3.2620.

In Table B.4, where n = 40 and i = 3%, the f = 75.4013.

Exercise B-18 (10 minutes)

a. p = present value of $60,000 at 9% for 4 years

p = $60,000 x 0.7084

p = $42,504

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

→The same answer results: choose $463 today

f = future value of $463 at 9% for 10 years

d. f = future value of $90 at 5% 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

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%.

OR