Question

You are planning to save for retirement over the next 25 years. To do this, you will invest $700 per month in a stock account and $300 per month in a bond account. The return of the stock account is expected to be an APR of 9 percent, and the bond account will earn an APR of 5 percent. When you retire, you will combine your money into an account with an APR of 6 percent. All interest rates are compounded monthly. How much can you withdraw each month from your account assuming a withdrawal period of 20 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Withdrawal $ 6910.13 (incorrect)per month

Answer 1

Monthly Withdrawl

$       6,902.45

per month

Working:

a.

Future Value of annuity of 1 @ 9%

=

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

Where,

=

(((1+0.0075)^300)-1)/0.0075

i

9%/12

=

0.0075

=

1121.1219

n

25*12

=

300

b.

Future Value of Stock Investment

=

Monthly investment x Future Value of annuity of 1

=

$           700.00

x

1121.1219

=

$ 7,84,785.36

c.

Future Value of annuity of 1 @ 5%

=

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

Where,

=

(((1+0.004167)^300)-1)/0.004167

i

5%/12

=

0.004167

=

595.5453

n

25*12

=

300

d.

Future Value of Bonds Investment

=

Monthly investment x Future Value of annuity of 1

=

$           300.00

x

595.5453

=

$ 1,78,663.58

e.

Combined Future Value of Investment

=

$ 7,84,785.36

+

$ 1,78,663.58

=

$ 9,63,448.94

f.

Present value of annuity of 1 @ 6%

=

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

Where,

=

(1-(1+0.005)^-240)/0.005

i

6%/12

=

0.005

=

139.5808

n

20*12

=

240

g.

Amount of monthly withdrawl

=

Total Accumulated amount at the beginning of withdrawl period/Present value of annuity of 1

=

$ 9,63,448.94

/

139.5808

=

6,902.45