Question

You want to retire in 38 years and have $100,000 currently saved in an account earning 9.5% interest. How much must you deposit into that account each month to be able to retire for 25 years and withdraw $500,000 per year if you are able to earn 5% during retirement?

Answer 1

Annuity Withdrawl Required (P)=	500000
interest rate (i)=	5%
time for Annuity withdrawl (n)=	25
Present Value of ordinary annuity formula = (Annuity *(1-(1/(1+i)^n))/i)
=500000*(1-(1/(1+5%)^25))/5%
=7046972.283
So fund needed at Retirement is	$7046972.28
Current deposit (present value) =	100000
interest rate (i)= 9.5% number of years (n) = 38 future value = present value *(1+i)^n =100000*(1+9.5%)^38 =3145839.264
Ballance Future value required to be saved =7046972.28- 3145839.26	3901133.02
Time in years (n) =	38
interest rate (i)=	9.5%
Amount required to save each year Formula = Future value*i/(((1+i)^n)-1)
3901133.02*9.5%/(((1+9.5%)^38)-1)
12167.6689
So annual Contribution needed is	$12167.67