You are planning to save for retirement over the next 26 years. To save for reti

Question

You are planning to save for retirement over the next 26 years. To save for retirement, you will invest $680 a month in a stock account in real dollars and $320 a month in a bond account in real dollars. The effective annual return of the stock account is expected to be 13 percent, and the bond account will earn 6 percent. When you retire, you will combine your money into an account with an 10 percent effective return. The inflation rate over this period is expected to be 5 percent. Assuming a 28-year withdrawal period you can withdraw $__________each month from your account in real terms. The nominal dollar amount of your last withdrawal is $ ____________.

Explanation / Answer

1) If you deposit $690 REAL dollars monthly for 26 years at a NOMINAL rate of 14%, you will have $1,724,995.11 REAL dollars after the 26 years (since inflation has already been taken into account by putting the deposit in REAL terms... I think so anyway). 2) If you deposit $240 REAL dollars monthly for 26 years at a NOMINAL rate of 9%, you will have $268,773.05 REAL dollars after the 26 years. 3) Combine those numbers and you will have $1,993,768.17 REAL dollars when you retire. 4) The REAL rate for the following 22 years is (1.10/1.03)-1 = 6.7961% per YEAR. 5) Now to find the monthly withdrawal amount: PV = $1,993,768.17 FV = $0 N = 22*12 = 264 Int = 6.7961/12 = 0.5663% PMT = ??? 6) The answer is you withdraw $14,572.84 REAL dollars each month for 22 years. 7) The nominal amount of the final withdrawal (if I'm reading that correctly) would be that amount multiplied by the MONTHLY inflation rate which will have compounded 264 times. So: $14,572.84*(((1+(.03/12))^264) = $28,172.21 NOMINAL withdrawal in the final month of year 22.

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