Question

Janice plans to retire in 25 years and would like to receive $5000.00 per month for fifteen years starting at the end of the first month after her retirement. Calculate the amount she must invest now if interest is 7.5% compounded monthly.

Answer 1

Solution

Here We have to find out the Present value of the annuity payments she wants to recieve 25 years later at the time of retirement

PV of annuity=Annuity amount*((1-(1/(1+r)^n))/r)

where

r=interest rate per period=7.5/12=.625%

n= number of periods=15*12=180

Annuity amoun=$5000

PV of annuity=5000*((1-(1/(1+.00625)^180))/.00625)=539367.134

Thus the present value of the amount at the time of her retirement = 539367.134

This Present value should be equal to the amount she must have in her account at the time of retirement to have the annuity payments

Thus future value of amount deposited=Amount deposited today*(1+i)^m

where i=rate of interest per period=7.5/12=.625

n=number of periods=25*12=300

future value of amount deposited=539367.134

539367.134=Amount deposited today*(1+.00625)^300

Amount deposited today=83198.686

Thus she must invest 83198.686

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