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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?

Respuesta :

Answer:

withdraw each month is $6,902.37

Explanation:

given data

time = 25 year

invest = $700 per month

stock amount = $300 per month

expected rate = 9% = [tex]\frac{0.09}{12}[/tex]

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 = [tex]P \frac{(1+r)^t -1}{r}[/tex]      ...............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 =  [tex]700 \frac{(1+\frac{0.09}{12})^{25*12} -1}{\frac{0.09}{12}}[/tex]  

value of the stock account = $784,785.36

and

value of the bond account at retirement will be

value of the bond account =  [tex]300 \frac{(1+\frac{0.05}{12})^{25*12} -1}{\frac{0.05}{12}}[/tex]  

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 = [tex]\frac{Pv}{\frac{1- \frac{1}{(1+r)^t}}{r} }[/tex]      ...............2

amount = [tex]\frac{963438.27}{\frac{1- \frac{1}{(1+\frac{0.06}{12})^{20*12}}}{\frac{0.06}{12}} }[/tex]  

amount =  $6,902.37

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