You want to have $6 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 13 percent and the inflation rate is 5.1 percent.
What real amount must you deposit each year to achieve your goal?
To determine the real amount you must deposit each year to achieve your goal, you need to take into account the effects of inflation. Here's how you can calculate it:
Step 1: Calculate the future value of $1 to account for the effects of inflation. Since the inflation rate is 5.1 percent, the future value factor is (1 + 0.051) = 1.051.
Step 2: Calculate the nominal return on your investment by adding the inflation rate to the desired real return. In this case, the desired real return is 13 percent, so the nominal return is (13 + 5.1) = 18.1 percent or 0.181.
Step 3: Determine the annual deposit you need to make to achieve your goal. To do this, divide the desired future value ($6 million) by the future value of $1 over the investment period, assuming a nominal return of 0.181.
So, the formula to calculate the annual deposit is:
Annual deposit = Desired future value / Future value of $1
Annual deposit = $6,000,000 / [(1.051)^40 * (1.181^40)]
By plugging the values into a calculator, you can find the annual deposit amount that would allow you to achieve your goal of having $6 million in real dollars in 40 years.
Note: It's important to understand that these calculations involve assumptions about future inflation and investment returns, and actual results may vary. It's always a good idea to consult with a financial advisor for personalized advice.