In wisely planning for your retirement, you invest $12,000 per year for 20 years into a 401k account. How much will you be able to withdraw each year for 10 years, starting one year after your last deposit, if you can earn a real return of 10% per year and the inflation rate averages 2.8% per year?

Annual withdraw= $173,483.28

Explanation:

The real rate of return is the result of deducting from the nominal rate the inflation rate.

First, we will determine the nominal rate of return:

Nominal rate= 0.10 + 0.028= 0.128

Now, we need to calculate the value of the investment at the time of retirement:

Annual deposit= $12,000

Interest rate= 0.128

Number of periods= 20 years

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

A= annual deposit

FV= {12,000*[(1.128^20) - 1]} / 0.128

FV= $948,935.34

Finally, the annual withdrawal:

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

Annual withdraw= (948,935.34*0.128) / [1 - (1.128^-10)]

Annual withdraw= $173,483.28

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