Question

A woman, with her employer’s matching program, contributes $200 at the end of each month to her retirement account, which earns 8% interest, compounded monthly. When she retires after 48 years, she plans to make monthly wothdrawals for 35 years. If her account earns 6% interest, compunded monthly, then when she retires, what is her maximum possible monthly withdrawal (without running out of kindh)?

Answer 1

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)
C= Periodic cash out flow.
r =effective interest rate for the period.
n = number of periods.

1.
FV= 200× {[(1+0.0066667)^576]-1}/0.00666667)
FV = $1,348,090.31

FV = Future value (The cummulative amount available in Future)
C= Periodic cash out flow = 200
r =effective interest rate for the period. =8%/12 =0.666667
n = number of periods = 48 x 12= 576

Retirement Money = $1,348,090.31

Formula: The present value of an ordinary annuity (PV)

PV = C× [1-(1+r)^-n]/r

PV = Present value (The cummulative amount available at retirement)
C= Periodic cash flow.
r =effective interest rate for the period.
n = number of periods.

$1,348,090.31= C× [1-(1+0.005)^-420]/0.005

PV = $1,348,090.31.
C= Periodic monthly withdrawals.
r =effective interest rate for the period= 6/12= 0.5% =0.005
n = number of periods. 35 x 12= 420

C= $7686.67

the maximum possible monthly withdrawal is $7686.67