Question

# You want to retire in 38 years and have \$100,000 currently saved in an account earning...

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?

 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