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 on your investment.
First, let's calculate the nominal rate of return adjusted for inflation by subtracting the inflation rate from the nominal return rate:
Nominal return rate - Inflation rate = 13% - 5.1% = 7.9%
Next, we'll use the future value of an annuity formula to calculate the annual deposit needed. The formula is:
R = (FV / (((1 + r)^n) - 1)) * (1 - (1 + i)^-n)
Where:
R = Annual deposit amount
FV = Future value goal ($6 million)
r = Nominal return rate adjusted for inflation (7.9% or 0.079)
n = Number of periods (40 years)
i = Inflation rate (5.1% or 0.051)
Plugging in the values:
R = ($6,000,000 / (((1 + 0.079)^40) - 1)) * (1 - (1 + 0.051)^-40)
Using a financial calculator or spreadsheet, the result is:
R ≈ $21,303.19
Therefore, to achieve your goal of having $6 million in real dollars when you retire in 40 years, you would need to deposit approximately $21,303.19 each year.
To calculate the real amount you need to deposit each year, we first need to account for inflation. The inflation rate is given as 5.1 percent annually. This means that the value of money decreases by 5.1 percent each year.
Next, we need to consider the nominal return on your investment, which is 13 percent. The nominal return represents the total return on your investment without accounting for inflation.
To determine the real return on your investment, we subtract the inflation rate from the nominal return. In this case, the real return would be 13 percent - 5.1 percent = 7.9 percent.
The future value of annuity formula can be used to calculate the real amount you need to deposit each year. The formula is:
FV = P * (((1 + r)^n - 1) / r)
Where:
FV = Future value of the annuity
P = Annual deposit
r = Real return
n = Number of years
In this case, we want to find the annual deposit (P), so we rearrange the formula:
P = FV / (((1 + r)^n - 1) / r)
Now, let's plug in the given values into the formula:
FV = $6,000,000 (future value)
r = 7.9% (real return)
n = 40 years
P = $6,000,000 / (((1 + 0.079)^40 - 1) / 0.079)
Simplifying the equation and calculating it will give us the real amount you need to deposit each year.