Question

You are planning to save for retirement over the next 25 years. To do this, you will invest $1,000 a month in a stock account and $700 a month in a bond account. The return of the stock account is expected to be 9 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with a return of 7 percent. How much can you withdraw each month from your account assuming a 20-year withdrawal period

Answer 1

Monthly withdraw= $12,452.6

Step-by-step explanation:

First, we need to calculate the total accumulated at the moment of retirement. We will use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

Stock:

Monthly investment= $1,000

Interest rate= 0.09/12= 0.0075

Number of periods= 25*12= 300 months

FV= {1,000*[(1.0075^300) - 1]} / 0.0075

FV= $1,121,121.94

Bond:

Monthly investment= $700

Interest rate= 0.06/12= 0.005

Number of periods= 25*12= 300 months

FV= {700*[(1.005^300) - 1]} / 0.005

FV= 485,095.77

Total FV= 1,121,121.94 + 485,095.77

Total FV= $1,606,217.71

Now, the annual withdrawal:

Interest rate= 0.07/12= 0.005833

Number of months= 12*20= 240

Monthly withdraw= (FV*i) / [1 - (1+i)^(-n)]

Monthly withdraw= (1,606,217.71*0.005833) / [1 - (1.005833^-240)]

Monthly withdraw= $12,452.6