You want to have $3 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 10 percent and the inflation rate is 4.8 percent. What real amount must you deposit each year to achieve your goal

Annual deposit= $23,647.9

Explanation:

Giving the following information:

Future value (FV)= 3,000,000

Numer of periods (n)= 40 years

Nominal rate= 10%

Inflation rate= 4.8%

To simplify calculations, we will calculate the real interest rate by deducting from the nominal interest rate the inflation rate:

Real interest rate= 0.1 - 0.048

Real interest rate= 0.052

Now, to calculate the annual deposit, we need to use the following formula:

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

A= annual deposit

Isolating A:

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

A= (3,000,000*0.052) / [(1.052^40) - 1]

A= $23,647.9

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