Question

In: Math

20. You want to be able to withdraw $25,000 from your account each year for 30...

20. You want to be able to withdraw $25,000 from your account each year for 30 years after you retire. If you expect to retire in 15 years and your account earns 7.4% interest while saving for retirement and 5.3% 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? $

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 = $ 25000, r = 5.3/100 = 0.053 and n = 30. Hence 25000 = 0.053(PV) /[ (1-(1.053)^-30] or, PV = (25000/0.053) [ (1-(1.053)^-30] = (25000/0.053) * (1-0.212397237) = (25000/0.053)*0.787602762 = $ 371510.74( on rounding off to the nearest cent). Thus, $ 371510.74 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= $ 371510.74, r = 7.4/1200 and n = 15*12 =180. Hence 371510.74 = (1200P/7.4)[ (1207.4/1200)¹⁸⁰ -1] = (1200P/7.4)* (3.024033409-1) = (1200P/7.4)* 2.024033409 so that P = [371510.74*7.4]/[1200*2.024033409] = $ 1131.89 ( on rounding off to the nearest cent). Thus, the amount that needs to be deposited each month until retirement is $1131.89.

c). The amount deposited into the retirement account is 180* $ 1131.89 = $ 203740.20 ( on rounding off to the nearest cent).

d). The amount received in payments during retirement is 30* $ 25000 = $ 750000.

e). The part of the money that was received via interest is $ 750000 -$203740.20 = $ 546259.80.

a) How much will you need to have when you retire? $ 371510.74.

b) How much will you need to deposit each month until retirement to achieve your retirement goals? $1131.89.

c) How much did you deposit into your retirement account? $ 203740.20.

d) How much did you receive in payments during retirement? $ 750000.

e) How much of the money you received was interest? $ 546259.80..

milcah answered 2 years ago

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