Question

You are planning your retirement in 15 years. You plan to retire with $3,000,000 and your retirement account earns 4.8% compounded monthly. After you retire, you plan on withdrawing $15,000 per month from your account until you have nothing left. How many years can you live off your retirement account after you retire?

Answer 1

Answer:

The retirement fund will last for 33 years and 7 months

Explanation:

We need to solve for time in an ordinary annuity

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C  $15,000.00

rate 0.004 (4.8% divide by 12 month)

PV $3,000,000

time n

$15,000 \times \frac{1-(1+0.004)^{-n} }{0.004} = 3,000,000$

we clear for n as much as we can and solve

$(1+0.004)^{-n}= 1-\frac{3,000,000\times0.004}{15,000}$

$(1+0.004)^{-n}= 0.20$

now we use logarithmic properties to solve for n:

$-n= \frac{log0.2}{log(1+0.004)$

-403.16  

this will be a value in months so we divide by 12 to get it annually

403/12 = 33,5833

we convert the residual to months:

0.5833 x 12 = 6.996 = 7 months