Question

What is the future worth of a series of equal quarterly payments of $25,000 if the series extends for six years at APR=8% ... a. (5 pts) Compounded quarterly (4 quarters per year)? b. (5 pts) Compounded monthly (3 months per quarter)? c. (5 pts) Compounded weekly (13 weeks per quarter)?

Answer 1

Future Worth of series of equal quarterly payment:

a.

If compounded quarterly

$ 7,60,546.56

b.

If compounded Monthly

$ 7,61,787.84

c.

If compounded Weekly

$ 7,62,271.82

Working:

a.

If compounded quarterly

1)

Future Value of annuity of 1

=

(((1+i)^n)-1)/i

Where,

=

(((1+0.02)^24)-1)/0.02

i

8%/4

=

2%

=

30.42186

n

6*4

=

24

2)

Future Value of annuity of $25,000

=

$     25,000.00

x

30.42186

=

$ 7,60,546.56

b.

If compounded Monthly

1)

Effective quarterly rate

=

((1+(i/n))^n)-1

Where,

=

((1+(0.02/3))^3)-1

i

quarterly rate

2%

=

0.02013363

n

Compounding per quarter

3

2)

Future Value of annuity of 1

=

(((1+i)^n)-1)/i

Where,

=

(((1+0.02013363)^24)-1)/0.02013363

i

0.02013363

=

30.47151

n

6*4

=

24

3)

Future Value of annuity of $25,000

=

$     25,000.00

x

30.47151

=

$ 7,61,787.84

c.

If compounded Weekly

1)

Effective quarterly rate

=

((1+(i/n))^n)-1

Where,

=

((1+(0.02/13))^13)-1

i

quarterly rate

2%

=

0.020185661

n

Compounding per quarter

13

2)

Future Value of annuity of 1

=

(((1+i)^n)-1)/i

Where,

=

(((1+0.02018566)^24)-1)/0.02018566

i

0.02018566

=

30.49087

n

6*4

=

24

3)

Future Value of annuity of $25,000

=

$     25,000.00

x

30.49087

=

$ 7,62,271.82