Question

You want to have $1 million in real dollars in an account when you retire in 30 years. The nominal return on your investment is 9 percent and the inflation rate is 4 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

Step 1 - Calculation of real rate of return
Real rate of return = [(1+Nominal rate) / (1+Inflation rate)] - 1
Real rate of return = [(1+0.09) / (1+0.04)] - 1
Real rate of return = 4.81%
Step 2 - Calculation of real Deposit amount each year to have $1 million in real dollars in an account when you retire in 30 years.
We can use the future value of annuity formula to calculate the deposit amount
Future value of annuity = P * {[(1+r)^n -1]/r}
Future value of annuity = $1 million i.e.$10,00,000
P = Yearly deposit amount = ?
r = real rate of return = 4.81%
n = no.of years = 30
1000000 = P * {[(1+0.0481)^30 -1]/0.0481}
1000000 = P*64.286
P = 15555.49
Deposit amount = $15,555.49