22. Problem 6-32 Calculating Annuities[LO1] You are planning to save for retirem

Question

22. Problem 6-32 Calculating Annuities[LO1] You are planning to save for retirement over the next 30 years. To do this, you will invest $890 a month in a stock account and $490 a month in a bond account The return of the stock account is expected to be 10.9 percent and the bond account will pay 6.9 percent. When you retire, you will combine your money into an account with a 79 percent return. How much can you withdraw each month from your account assuming a 25-year withdrawal period? (Do not round Intermediate calculations and round your final answer to 2 decimal places, (e.g., 32.16)) Withdrawal $ per month

Explanation / Answer

FV interest factor of annuity = [(1+i)n-1]/i

FV of stock account = 890 * FV interest factor of annuity = 890 * [(1+10.9%)30 - 1]/10.9% = 173,767.1973

FV of bound account = 490 * FV interest factor of annuity = 490 * [(1+6.9%)30 - 1]/6.9% = 45,461.3088

total money = 173,767.1973 + 45,461.3088 = 219,228.5061

$219,228.5061 is the PV of the 25-year withdraw period

PV interest factor of annuity = [1-(1+i)-n]/i

219,228.5061 = A [1-(1+i)-n]/i = A [1-(1+7.9%)-25]/7.9%

A = $20,361.92

therefore, you can withdraw $20,361.92 each month

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