In: Finance
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?
$
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