Question

For the next 20 years, you plan to invest $600 a month in a stock account earning 7 percent annually and $400 a month in a bond account earning 4 percent per year. When you retire in 20 years, you will combine your money into an account with a return of 10 percent per year. How much can you withdraw each month during retirement assuming a 30-year withdrawal period?

Answer 1

Answer:

Monthly withdraw= $204.55

Step-by-step explanation:

First, we need to calculate the value of the account at the moment of retirement using the following formula:

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

A= monthly deposit

Stock:

Monthly deposit= $600

Interest rate= 0.07/12= 0.00583

Number of periods (n)= 20*12= 240 months

FV= {600*[(1.00583^240) - 1]} / 0.00583

FV= $312,404.24

Bond:

Monthly deposit= $400

Interest rate= 0.04/12= 0.0033

Number of periods (n)= 20*12= 240 months

FV= {400*[(1.0033^240) - 1]} / 0.0033

FV= $146,052.20

Total value at retirement= $458,456.44

Now, we can determine the monthly withdrawals after retirement:

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

FV= 458,456.44

n= 30*12= 360

i= 0.1/12= 0.0083

Monthly withdraw= (458,456.44*0.0083) / [(1.0083^360) - 1]

Monthly withdraw= $204.55