You want to be able to withdraw $20,000 from your account each year for 30 years...

You want to be able to withdraw $20,000 from your account each year for 30 years after you retire. If you expect to retire in 25 years and your account earns 6.8% interest while saving for retirement and 4.4% 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?
$

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Solutions

Expert Solution

a) The formula for a fixed no. of annuity paments(P) is P = r (PV)/[1-(1+r)^-n] where PV is the present value, r is the interest rate per period and n is the no. of periods.

Here, P = $ 20000, r = 4.4 % = 44/1000 = 11/250 and n = 30 so that 20000 = (11/250)PV [1- (1+11/250)^-30] = (11/250)PV/(0.72522005). Hence PV = 20000*(0.72522005)*250/11 = $ 329645.48 ( on rounding off to the nearest cent). Thus, a sum of $ 329645.48 is needed at the time of retirement.

b). The formula for the future value (F) of annuity is F = P[(1+r)ⁿ-1]/r where P is periodic payment, r is the interest rate per period and n is the no. of periods. Here, 329645.48 = [P/(68/12000)][(1+68/12000)^25*12 -1] = [12000P/(68)](4.447743322) so that P = 329645.48*68*(1/4.447743322)*(1/12000)]= $ 419.99. Thus, there is a need to deposit $ 419.99 each month until retirement.

c). The amount deposited into the retirement a/c is $419.99*300 = $ 125997.

d). The amount received in payments during retirement is $ 20000 *30 = $ 600000.

e). The amount received as interest is $ 600000-$125997 = $ 474003.

milcah answered 1 year ago

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