You want to have $2million in real dollars in an account when you retire in 43 years. The nominal return on your investment in 9.939% and the inflation rate is 3.2%. What is the real amount you must deposit each year to achieve this goal?
The first thing to do is to use the fisher rule, which implies:
(1+R)= (1+r)*(1+h); h being inflation.
So, (1+0.09939)= (1+r)* (1+0.032)
(1+r)= (1.09939)/(1.032)
r= 1- 1.0653= 6.53%
Take you Financial calculator and put the following order:
I/Y= 6.53
N=43
FV= 2,000,000
PV=0
CPT+PMT= 9,209.68
To calculate the real amount you must deposit each year to achieve your retirement goal, you need to account for inflation and the nominal return on your investment. Here are the steps to solve this:
1. Adjust for inflation: Convert the nominal return rate to the real return rate by subtracting the inflation rate. In this case, the real return rate is 9.939% - 3.2% = 6.739%.
2. Calculate the future value: Use the future value formula to determine the amount you need to accumulate by the time of retirement. The formula is:
Future Value = Present Value × (1 + Real Return Rate)^Number of Years
In this case, the future value you want to achieve is $2 million, the present value is the annual deposit you want to find, the real return rate is 6.739%, and the number of years is 43.
$2,000,000 = Annual Deposit × (1 + 0.06739)^43
3. Solve for the annual deposit: Rearrange the formula to solve for the annual deposit:
Annual Deposit = $2,000,000 / [(1 + 0.06739)^43]
Use a calculator or a spreadsheet program to compute the result.
By following these steps, you can calculate the real amount you must deposit each year to achieve your retirement goal of $2 million in 43 years, considering the nominal return on your investment and the inflation rate.
To calculate the real amount you must deposit each year to achieve your retirement goal, we need to adjust for inflation.
First, let's determine the real rate of return, which accounts for inflation. This is calculated by subtracting the inflation rate from the nominal return rate:
Real Rate of Return = Nominal Return - Inflation Rate
Real Rate of Return = 9.939% - 3.2%
Real Rate of Return = 6.739%
Next, we can use the future value of an ordinary annuity formula to find the deposit amount:
Future Value = Deposit Amount * ((1 + Real Rate of Return) ^ Number of Years - 1) / Real Rate of Return
Rearranging the formula, we can solve for the deposit amount:
Deposit Amount = Future Value * (Real Rate of Return) / ((1 + Real Rate of Return) ^ Number of Years - 1)
Substituting the given values:
Future Value = $2,000,000
Real Rate of Return = 6.739%
Number of Years = 43
Deposit Amount = $2,000,000 * (0.06739) / ((1 + 0.06739) ^ 43 - 1)
Using a calculator to evaluate the expression on the right side of the equation:
Deposit Amount ≈ $14,978.84
Therefore, you would need to deposit approximately $14,978.84 annually to achieve your retirement goal of $2 million in real dollars in 43 years, considering a nominal return of 9.939% and an inflation rate of 3.2%.