You want to be able to withdraw $50,000 from your account each year for 20 years...

You want to be able to withdraw $50,000 from your account each year for 20 years after you retire. If you expect to retire in 30 years and your account earns 5% interest while saving for retirement and 4.1% 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? $

Solutions

Expert Solution

a). The annuity payment formula is P = [r(PV)]/[ 1-(1+r)^-n] where P is the payment, PV is the present value, r is the rate of interest per period and n is the number of periods.

Here, P = $ 50000, r = 4.1/100 = 0.041 and n = 20. Hence 50000 = 0.041(PV) /[ (1-(1.041)^-20] or, PV = (50000/0.041) [ (1-(1.041)^-20] = (50000/0.041) * (1- 0.447698263) = (50000/0.041)*0.552301736 = $ 673538.70 ( on rounding off to the nearest cent). Thus, $ 673538.70 will be needed at the time of reirement.

b). The formula for computing the future value of an annuity(F) is F = (P/r)[ (1+r)ⁿ -1] where P is the periodic payment, r is the rate of interest per period and n is the number of periods.

Here, F = $ 673538.70, r = 5/1200 and n = 30*12 = 360. Hence 673538.70 = (1200P/5)[ (1205/1200)³⁶⁰ -1] = (1200P/5)* (4.467744319-1) = (1200P/5)* 3.467744319 so that P = [673538.70*5]/[1200*3.467744319 ] = $ 809.07 ( on rounding off to the nearest cent). Thus, the amount that needs to be deposited each month until retirement is $ 809.07.

c). The amount deposited into the retirement account is 360 * $ 809.07 = $ 291266.59 ( on rounding off to the nearest cent).

d). The amount received in payments during retirement is 20* $ 50000 = $ 1000000.

e). The part of the money that was received via interest is $ 1000000 -$ 291266.59 = $ 708733.41.

a) How much will you need to have when you retire? $ 673538.70.

b) How much will you need to deposit each month until retirement to achieve your retirement goals? $ 809.07.

c) How much did you deposit into your retirement account? $ 291266.59.

d) How much did you receive in payments during retirement? $ 1000000.

e) How much of the money you received was interest? $ 708733.41.

milcah answered 1 year ago

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