You want to have $1.5 million in real dollars in a retirement account when you retire in 40 years. The inflation rate is 2.7% and the nominal rate of return on your investment is 10%. What real amount must you deposit each year in the account to achieve your goal?

Annual deposit = $6,952.82

Explanation:

Giving the following information:

You want to have $1.5 million in real dollars in a retirement account when you retire in 40 years.

Inflation rate = 2.7%

Interest rate = 10%

First, we need to deduct from the interest rate the inflation rate.

Real interest rate = 0.10 - 0.027 = 0.073

Now, using the following formula, we can determine the annual deposit:

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

A = annual deposit

Isolating A:

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

A = (1,500,000*0.073) / [ (1.073^40) - 1]

A = $6,952.82