you decide to open an individual retirement account IRA at y

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? $

Solution

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