Question

You are planning to save for retirement over the next 30 years. To do this, you will invest $700 a month in a stock account and $400 a month in a bond account. The return of the stock account is expected to be 7.5 percent, and the bond account will pay 5.5 percent. When you retire, you will combine your money into an account with a 2.5 percent return. How much can you withdraw each month from your account assuming a 25-year withdrawal period?

a. 5.545.73.
b. 6,081.31.
c. 5,870.85.
d. 6.205.66

Answer 1

Monthly withdraw= $5,870.6

Step-by-step explanation:

Giving the following information:

Stock:

Monthly deposit= $700

Interest rate= 0.075/12= 0.00625

Number of periods= 30*12= 360

Bond:

Monthly deposit= $400

Interest rate= 0.055/12= 0.0045833

Number of periods= 30*12= 360

First, we need to calculate the value of the investment at the moment of retirement:

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

A= monthly deposit

Stock:

FV= {700*[(1.00625^360) - 1]} / 0.00625

FV= $943,211.797

Bond:

FV= {400*[(1.00458^360) - 1]} / 0.00458

FV= $365,447.415

Total FV= $1,308,659.212

Now, the monthly withdrawal:

Interest rate= 0.025/12= 0.002083

Number of periods= 25*12= 300

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

Monthly withdraw= (1,308,659.212*0.002083) / [1 - (1.002083^-300)]

Monthly withdraw= $5,870.6