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

Answer 1

withdraw each month is $6,902.37

Step-by-step explanation:

given data

time = 25 year

invest = $700 per month

stock amount = $300 per month

expected rate = 9% =
`(0.09)/(12)`

bond account = 5%

return = 6%

to find out

withdraw each month from account for 20 year withdrawal period

solution

we will apply here future value formula that is

FV =
`P ((1+r)^t -1)/(r)` ...............1

here P is principal amount i.e $700 given and r is are and t is time

so

The value of the stock account at retirement will be

value of the stock account =
`700 ((1+(0.09)/(12))^(25*12) -1)/((0.09)/(12))`

value of the stock account = $784,785.36

and

value of the bond account at retirement will be

value of the bond account =
`300 ((1+(0.05)/(12))^(25*12) -1)/((0.05)/(12))`

value of the bond account = $178,652.91

and

so value of the two accounts combined is here

= $178,652.91+$784,785.36 = $963,438.27

so

monthly withdrawal from combined account is

amount =
`(Pv)/((1- (1)/((1+r)^t))/(r) )` ...............2

amount =
`(963438.27)/((1- (1)/((1+(0.06)/(12))^(20*12)))/((0.06)/(12)) )`

amount = $6,902.37