Question

You want to have $4.5 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 6.5 percent. What real amount must you deposit each year to achieve your goal?

Answer 1

Desired Sum after 30 years = $4,500,000

Nominal Interest Rate = 13.00%
Inflation Rate = 6.50%

Real Interest Rate = (Nominal Interest Rate - Inflation Rate) / (1 + Inflation Rate)
Real Interest Rate = (0.13 - 0.065) / (1 + 0.065)
Real Interest Rate = 6.10%

Annual Deposit * FVIFA(6.10%, 30) = $4,500,00
Annual Deposit * (1.0610^30 - 1) / 0.0610 = $4,500,000
Annual Deposit * 80.46371 = $4,500,000
Annual Deposit = $55,926

So, annual deposit made to achieve your goal is $55,926