You want to have $5 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 12 percent and the inflation rate is 5 percent.
What real amount must you deposit each year to achieve your goal?
To calculate the amount you need to deposit each year to achieve your goal of having $5 million in real dollars when you retire, you'll need to consider the effect of inflation on your investment returns.
Here's how you can calculate the real amount you need to deposit each year:
1. Find the nominal return: Subtract the inflation rate from the nominal return. In this case:
Nominal Return = 12% - 5% = 7%
2. Adjust for inflation: Divide 1 by the sum of 1 plus the inflation rate. In this case:
Inflation Adjustment = 1 / (1 + 5%) = 1 / 1.05 = 0.95238
3. Calculate the real return: Multiply the nominal return by the inflation adjustment. In this case:
Real Return = 7% * 0.95238 = 6.66666%
4. Calculate the annual deposit: Divide the desired future value ($5 million) by the present value of a growing annuity, where the growth rate is the real return. The present value formula for a growing annuity is:
Annual Deposit = Future Value / [((1 + Real Return)^(Number of Years) - 1) / Real Return]
Plugging in the values, and assuming you start making deposits at the end of each year, the calculation would be:
Annual Deposit = $5,000,000 / [((1 + 6.66666%)^40 - 1) / 6.66666%]
By performing this calculation, you'll find the real amount you need to deposit each year to achieve your goal of $5 million in real dollars when you retire in 40 years.