Question

you are planning to save for retirement over the next 30 years. To save for retirement, you will invest $700 per month in a stock account in real dollars and $325 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will have an annual return of 7 percent. When you retire, you will combine your money into an account with an effective annual return of 8 percent. The inflation rate over this period is expected to be 4 percent. How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? what is the nominal dollar amount of your last withdrawl?

Answer 1

The effective annual return of the stock account is expected to be 12 percent, and the bond account will have an annual return of 7 percent.

The inflation rate over this period is expected to be 4 percent.

Real return = (1 + nominal return) / (1 + inflaton) - 1

Hence, real return on stock account = (1 + 12%) / (1 + 4%) - 1 = 7.69%

and the real return on bond account = (1 + 7%) / (1 + 4%) - 1 = 2.88%

FV of investment in stock account: Can be calculated using the FV function of excel. Inputs are:

Rate = 7.69%/12 = 0.64%; Nper = 30 x 12 = 360; PMT = -700; PV = 0

Hence, FV of stock account = FV (Rate, Nper, PMT, PV) = FV (0.64%, 360, -700, 0) = $ 980,337.29

FV of investment in bond account: Can be calculated using the FV function of excel. Inputs are:

Rate = 2.88%/12 = 0.24%; Nper = 30 x 12 = 360; PMT = -325; PV = 0

Hence, FV of stock account = FV (Rate, Nper, PMT, PV) = FV (0.24%, 360, -325, 0) = $ 185,690.94

Total amount at the time of retirement =  980,337.29 + 185,690.94 = 1,166,028.23

Monthly withdawl can be calculated using PMT function Inputs are:

Rate = 8% / 12 = 0.67%; Nper = 25 years x 12 = 300 months, PV = - 1,166,028.23; FV = 0

Hence, monthly withdrawl = PMT (Rate, Nper, PV, FV) = PMT (0.67%, 300, -1166028.23, 0) = $ 8,999.59

Hence, you can withdraw $ 8,999.59 (please do round it off as per your requirement) each month from your account in real terms assuming a 25-year withdrawal period.

The nominal dollar amount of your last withdrawl = Withdrawl in real terms x (1 + inflation)n

= 8,999.59 x (1 + 4%)(30 + 25) = $ $77,813.80