You want to have $4 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 11 percent and the inflation rate is 4.9 percent.

You want to have $4 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 11 percent and the inflation rate is 4.9 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

$

 

Explanation:

We first need to find the real interest rate on the savings. Using the Fisher equation, the real interest rate is:

(1 + R) = (1 + r)(1 + h)

1 + .11 = (1 + r)(1 + .049)

r = .0582, or 5.82%

Now we can use the future value of an annuity equation to find the annual deposit. Doing so, we find:

FVA = C{[(1 + R)t − 1] / R}

$4,000,000 = $C[(1.058230 − 1) / .0582]

C = $52,266.06