Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $800 per month in a stock account in real dollars and $400 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 11 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an effective return of 9 percent. The returns are stated in nominal terms. 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

What is the nominal dollar amount of your last withdrawal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Real return on stock account = (1 + nominal return) / (1 + inflation) - 1 = (1 + 11%) / (1 + 4%) - 1 = 6.73%

Real return on bond account = (1 + nominal return) / (1 + inflation) - 1 = (1 + 7%) / (1 + 4%) - 1 = 2.88%

Real return on combined account = (1 + nominal return) / (1 + inflation) - 1 = (1 + 9%) / (1 + 4%) - 1 = 4.81%

The amount in retirement account at the end of 30 years from now is calculated using FV function in Excel :

Stock account :

rate = 6.73% / 12 (converting annual return into monthly return)

pmt = 30 * 12 (30 years of deposits with 12 monthly deposits each year)

pmt = 800

FV is calculated to be $925,680.96

Bond account :

rate = 2.88% / 12 (converting annual return into monthly return)

pmt = 30 * 12 (30 years of deposits with 12 monthly deposits each year)

pmt = 400

FV is calculated to be $228,542.70

Total amount in retirement account after 30 years =  $925,680.96 + $228,542.70 = $1,154,223.65

Monthly withdrawal during 25-year period is calculated using PMT function in Excel :

rate = 4.81% / 12   (converting annual return of combined account into monthly return)

nper = 25 * 12   (25 years of withdrawals with 12 monthly withdrawals each year)

pv = 1,154,223.65 (starting amount in retirement account at the start of the 25-year period)

PMT is calculated to be $6,618.79

Nominal dollar amount of last withdrawal = real dollar amount of last withdrawal * (1 + inflation rate)⁵⁵ (we use 55 years because the last withdrawal is 55 years from now)

Nominal dollar amount of last withdrawal = $6,618.79 * (1 + 4%)⁵⁵ = $57,228.47