You want to be able to withdraw $45,000 from your account each year for 15 years...

You want to be able to withdraw $45,000 from your account each year for 15 years after you retire. If you expect to retire in 25 years and your account earns 6.8% interest while saving for retirement and 6.5% 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

the present value of ordinary annuity formula

1. PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount need at retirement)
C= Periodic cash flow. 45000
r =effective interest rate for the period. 6.5%or 0.065
n = number of periods. 15

PV = 45000× [1-(1+0.065)^-15]/0.065

PV=$423,120.09

How much will you need to have when you retire?
$423,120.09

2. Formula: The Future Value of an ordinary annuity (FV)

FV= C× {[(1+r)^n]-1}/r

FV = Future value (The cummulative amount available in Future when person retirement) $423,120.09
C= Periodic cash out flow. ?
r =effective interest rate for the period. 0.068
n = number of periods. 25

$423,120.09= C× {[(1+0.068)^25]-1}/0.068

C=$6884.25

How much will you need to deposit each month until retirement to achieve your retirement goals? $6884.25

c. How much did you deposit into you retirement account?$6884.25x25= $172,106.25

d) How much did you receive in payments during retirement?$423,120.09

e. ) How much of the money you received was interest?$423,120.09-$172,106.25= $251,013.84

jeff jeffy answered 4 months ago

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