Question

You are planning to save for retirement over the next 20 years. To do this, you will invest $1,100 a month in a stock account and $800 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a return of 8 percent. How much can you withdraw each month from your account assuming a 20-year withdrawal period?

A.120,943.05

B.9877.02

C.10,208.16

D.513,326.32

E.10,078.59

Answer 1

Amount invested in stock each month = S = $1100 at interest rate = r1 = 10%

Amount invested in Bond each month = B = $800 at interest rate = r2 = 6%

Number of investment periods = 20*12 = 240 months

Future Value of Stock account = S(1+r1)^n-1 +....+ S(1+r1)² + S(1+r1) + S = S[(1+r1)ⁿ -1]/r1 = 1100[(1+0.10/12)²⁴⁰ -1]/(0.10/12) = $835305.71

Future Value of Bond account = B(1+r2)^n-1 +....+ B(1+r2)² + B(1+r2) + B = B[(1+r2)ⁿ -1]/r2 = 800[(1+0.06/12)²⁴⁰ -1]/(0.06/12) = $369632.72

Total Value in account after 20 years = 835305.71 + 369632.72 = $1204938.43

Let the amount withdrawn each month be X

Interest rate = r = 8%

Number of withdrawal periods = n = 20*12 = 240 months

Present Value of all the withdrawals = X/(1+r) + X/(1+r)² +....+ X/(1+r)ⁿ = X[1- (1+r)^-n]/r = X[1- (1+0.08/12)^-240]/(0.08/12) = 119.554X

This should be equal to the investment value

=> 119.554X = 1204938.43

=> X = 10078.61

HEnce, (e) is the correct option