You are planning to save for retirement over the next 20 yea

You are planning to save for retirement over the next 20 years. To do this, you will invest $800 a month in a stock account and $500 a month in a bond account. The return of the stock account is expected to be 9 percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 7 percent return. Required: How much can you withdraw each month from your account assuming a 20-year withdrawal period?

Solution

(1) In the first step we shall compute the future value of monthly Investments.

FVIFA = [ (1+r)ⁿ - 1 ] / r

Here n = 20 Years * 12 = 240

r = return / 12

at 9% return ......... [ (1.00759)²⁴⁰ - 1 ] / 0.0075 = 667.886870

at 4% return ...........[ (1.0.00333333)²⁴⁰ - 1 ] / 0.00333333 = 366.774626

Future value = 800 * 667.886870 + 500 * 366.774626 = 717696.81

(2) In this second and last step we calculate monthly withdrawing from this fund invested at 7 %

For this compute the PVIFA ......... Present value of Interest factor annuity

= [ 1 - (1+r)^-n ] / r

= [ 1 - (1.00583333)^-240 ] / 0.00583333 = 128.98

Monthly withdrawal = Fund / PVIFA = 717696.81 / 129.98 = 5521.59 ........ Final answer