Question

you decide to open an individual retirement account (IRA) at your local bank that pays 11%/year/year. At the end of each of the next 40 years, you will deposit $2,500 per year into the account (40 total deposits). 3 years after the last deposit, you will begin making annual withdrawals. If you want the account to last 30 years (30 withdrawals), what amount will you be able to withdraw each year? $

Answer 1

First calculate the retirment corpus
FV of annuity
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / i)
Where:
P = the future value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
FV of annual contribution	=2500*((((1 + 11%) ^40) - 1) / 11%)
FV of annual contribution	1,454,565
Total corpus	1,454,565
This corpus remains invested for 3 Years
Corpus after 3 YEARS	=1454565*(1+11%)^3
Corpus after 3 YEARS	1,989,308
Now he will start withdrawing money from this fund for next 30 years
PV of annuity for making pthly payment
P = PMT x (((1-(1 + r) ^- n)) / i)
Where:
P = the present value of an annuity stream
PMT = the dollar amount of each annuity payment
r = the effective interest rate (also known as the discount rate)
i=nominal Interest rate
n = the number of periods in which payments will be made
1,989,308	=Annual withdrawl*(((1-(1 + 11%) ^-30)) /11%)
1,989,308	=Annual withdrawl * 8.693
Annual withdrawl=	=1989308/8.693
Annual withdrawl=	228,840