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

The retirement fund will last for 33 years and 7 months

Step-by-step explanation:

We need to solve for time in an ordinary annuity

`C * (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 * (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-(3,000,000*0.004)/(15,000)`

`(1+0.004)^(-n)= 0.20`

now we use logarithmic properties to solve for n:

-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