Question

You want to have $3 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 13 percent and the inflation rate is 3.7 percent. 

What real amount must you deposit each year to achieve your goal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) 

Deposit amount = _______ 

Answer 1

Real rate = [(1 + nominal rate) / (1 + inflation)] - 1

Real rate = [(1 + 0.13) / (1 + 0.037)] - 1

Real rate = 1.089682 - 1

Real rate = 0.089682 or 8.9682%

Future value = Annuity * [(1 + r)ⁿ - 1] / r

3,000,000 = Annuity * [(1 + 0.089682)³⁰ - 1] / 0.089682

3,000,000 = Annuity * 135.501503

Annuity = 22,139.98