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)

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)

In Table B.1, where n = 5 and i = 9%, the p = 0.6499.

Amount willing to pay today: 0.6499 x $140,000 = $90,986

Quick Study B-5 (10 minutes)

In Table B.2, where n = 10 and i = 12%, the f = 3.1058.

Cash proceeds at liquidation:3.1058 x $630,000 = $1,956,654

Quick Study B-6 (10 minutes)

In Table B.3, where n = 6 and i = 7%, the p = 4.7665.

Amount willing to pay for the project:4.7665 x $150,000 = $714,975

Quick Study B-7 (10 minutes)

In Table B.4, where n = 30 and i = 10%, the f = 164.494.

Ending value of the investment program:164.494 x $1,500 = $246,741

EXERCISES

Exercise B-1 (10 minutes)

In Table B.2, where i = 12% and f = $96,463/$10,000 = 9.6463, the n = 20 (implies the investor must wait 20 years before payment).

Exercise B-2 (10 minutes)

In Table B.2, where n = 25 and f = $108,347/$10,000 = 10.8347, the i = 10% (investor must earn 10% interest to achieve investment goal).

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)

In Table B.3, where i = 10% and p = $82,014/$10,000 = 8.2014, the n = 18 (investor expects 18 annual payments to be received).

Exercise B-5 (10 minutes)

In Table B.4, where n = 40 and f = $154,762/$1,000 = 154.762, the i = 6% (investor must earn a 6% rate of interest).

Exercise B-6 (10 minutes)

In Table B.4, where i = 8% and f = $303,243/$10,000 = 30.3243, the n = 16 (investor must make 16 annual payments to achieve investment goal).

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 =

$154,150

present value of maturity amount

17.2920 x $ 25,000 =

432,300

present value of interest payments

$586,450

cash proceeds

Exercise B-9 (15 minutes)

In Table B.1, where n = 6 and i = 10%, the p = 0.5645.

Present value of investment = $606,773 x .5645 = $342,523

Exercise B-10 (15 minutes)

1.$90,000 x 0.6651 (using Table B.1, i = 6%, n = 7) = $59,859.

2.$20,000 x 2.4869 (using Table B.3, i = 10%, n = 3) = $49,738.

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)

Single Future Payment

Number of Periods

Interest Rate

Table B.1 Value

Amount Borrowed

a.

$40,000

3

4%

0.8890

$35,560

b.

75,000

7

8

0.5835

$43,763

c.

52,000

9

10

0.4241

$22,053

d.

18,000

2

4

0.9246

$16,643

e.

63,000

8

6

0.6274

$39,526

f.

89,000

5

2

0.9057

$80,607

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

In Table B.2, where n = 40 and i = 2%, the f = 2.2080.

Total accumulation = 2.2080 x $7,200 = $15,897.60

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

In Table B.4, where n = 30 and i = 1%, the f = 34.7849.

Total accumulation = 34.7849 x $50 = $1,739.25

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.

3.2620 x $100,000 =

$326,200

future value of initial investment

75.4013 x $50,000=

3,770,065

future value of periodic investments

$4,096,265

future value of fund

Exercise B-18 (15 minutes)

In Table B.2, where n = 9 and i = 7%, the f = 1.8385.

Future value of investment = $163,170 x 1.8385 =$299,988

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

(1)Future Value of a single amount.

(2)Divide $10,000 by f from Table B.2.

(3)Use Table B.2, 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

(1)Present Value of an Annuity.

(2)Multiply $10,000 by p from Table B.1 and then divide by p from

Table B.3.

(3)Use Tables B.1 and B.3,periods = 8 and interest rate = 4%.

c.(1)Future Value of an Annuity.

(2)Multiply $4,000 by f from Table B.4.

(3)Use Table B.4, periods = 40 and interest = 8%.

d.(1)Present Value of an Annuity.

(2)Multiply $30,000 by p from Table B.3.

(3)Use Table B.3, periods = 20 and interest = 10%.

[Note: Students must recognize the present value of $225,000

received today is $225,000.]