Final answer:
To achieve a retirement goal of $2 million in 40 years with a 9% nominal return and 5% inflation rate, you need to deposit approximately $22,793.48 in real dollars each year.
Step-by-step explanation:
To determine the real amount you must deposit each year to achieve your retirement goal of $2 million in 40 years, you need to account for the effects of inflation on your savings. Since the nominal return on your investment is 9 percent and the inflation rate is 5 percent, the real rate of return is 4 percent (9% - 5%).
You can calculate the real amount you must deposit each year by using the future value of an annuity formula:
R = P * ((1+r)^n - 1) / r
Where R is the real amount you must deposit each year, P is the real purchasing power you want to accumulate ($2 million), r is the real rate of return (4%), and n is the number of years (40 years).
By plugging in the values, we get:
R = 2,000,000 * ((1+0.04)^40 - 1) / 0.04
R ≈ $22,793.48
Therefore, you need to deposit approximately $22,793.48 in real dollars each year to achieve your retirement goal of $2 million in 40 years.