You want to be able to withdraw $40,000 from your account each year for 15 years

Question

You want to be able to withdraw $40,000 from your account each year for 15 years after you retire. If you expect to retire in 25 years and your account earns 7.6% interest while saving for retirement and 6.9% interest while retired:
Round your answers to the nearest cent as needed.

a) How much will you need to have when you retire?
$

b) How much will you need to deposit each month until retirement to achieve your retirement goals?
$

c) How much did you deposit into you retirement account?
$

d) How much did you receive in payments during retirement?
$

e) How much of the money you received was interest

Explanation / Answer

a). The formula for a terminating fixed annuity payment is P = r(PV)/[(1+r)n]/[ (1+r)n -1] where P is the fixed periodic payment, r is the rate of interest per period, n is the number of periods and PV is the present value. Here, P = $ 40000, n=15, and r=6.9%=0.069.Then 40000=PV*0.069(1.069)15/[(1.069)15-1] = PV*0.069(2.72060554)/(1.72060554) so that PV=(40000/0.069)*(1.72060554/2.72060554)=$366628.85.

b). The formula for the future value of an annuity is FV = P[(1+r)n-1]/r, where P is the periodic payment, P is the fixed periodic payment, r is the rate of interest per period and n is the number of periods. Here, FV =$366628.85,r=7.6/1200=19/3000 and n=25*12=300 so that 366628.85 = P*(3000/19)* [(1+19/3000)300-1] =P*(3000/19)*(5.64596443).Then P= 366628.85*(19/3000)/5.64596443=$411.26.

c). The amount deposited into the retirement a/c is $411.26 *300 = $123378.

d). The amount received in payments during retirement is 15*$ 40000 = $ 600000.

e). The amount received as interest is $ 600000-$123378 = $ 476622.

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