Question

g You are planning to save for retirement over the next 33 years. To do this, you will invest $774 per month in a stock account and $328 per month in a separate bond account. The return of the stock account is expected to be 12%, and the bond account will pay 6%. When you retire, you will combine your money into an account with an expected 9% return. How much can you withdraw each month in retirement from your account assuming a 20-year withdrawal period

Answer 1

monthly distribution = $32,877.37

Step-by-step explanation:

we can use the future value of an annuity formula to determine how much money you will have once you retire:

effective interest rate:

1.12 = (1 + r)¹²

¹²√1.12 = ¹²√(1 + r)¹²

1.00949 = 1 + r

r = 0.949%

1.06 = (1 + r)¹²

¹²√1.06 = ¹²√(1 + r)¹²

1.00487 = 1 + r

r = 0.487%

FV annuity factor, 396 periods, 0.949% = 4,332.08311

FV annuity factor, 396 periods, 0.487% = 1,200.65629

FV = $774 x 4,332.08311 = $3,353,032.33

FV = $328 x 1,200.65629 = $393,815.26

total FV = $3,746,847.59

to determine the monthly distribution, we can use the present value of an annuity formula:

effective interest rate:

1.09= (1 + r)¹²

¹²√1.09 = ¹²√(1 + r)¹²

1.00721 = 1 + r

r = 0.721%

PV annuity factor, 240 periods, 0.721% = 113.96434

monthly distribution = $3,746,847.59 / 113.96434 = $32,877.37