Question

You are planning to save for retirement over the next 20 years. To do this, you will invest $900 a month in a stock account and $600 a month in a bond account. The return of the stock account is expected to be 9 percent, and the bond account will pay 5 percent. When you retire, you will combine your money into an account with a return of 7 percent.

How much can you withdraw each month from your account assuming a 20-year withdrawal period?

Multiple Choice

a)$78,868.22

b)$6,572.35

c)$373,037.17

d)$6,440.9

e)$6,703.8

Answer 1

Accumulated balance after 20 years
Investment in stock
Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
= $900[ (1+0.0075)^240 -1] /0.0075
= $900[ (1.0075)^240 -1] /0.0075
= $900[ (6.0092 -1] /0.0075]
= $6,01,098.18
Investment in bond
Future Value of an Ordinary Annuity
= C*[(1+i)^n-1]/i
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
= $600[ (1+0.004166666)^240 -1] /0.004166666
= $600[ (1.004166666)^240 -1] /0.004166666
= $600[ (2.7126 -1] /0.004166666]
= $2,46,620.18
Total balance after 20 years = $601098.18+246620.18
=847718.36
The amount can be withdrawn each month after 20 years
Present Value Of An Annuity
= C*[1-(1+i)^-n]/i]
Where,
C= Cash Flow per period
i = interest rate per period
n=number of period
847718.36= C[ 1-(1+0.00583333)^-240 /0.00583333]
847718.36= C[ 1-(1.00583333)^-240 /0.00583333]
847718.36= C[ (0.7524) ] /0.00583333
C = $6572.35
Correct Option : "b"