To calculate how much money will be in your retirement account by the time you reach age 65, we need to first determine how many years the money will be invested.
Since you are currently 27, and you will reach 65 in:
\( 65 - 27 = 38 \) years.
Now we can plug those values into the formula you provided:
\[ A = 10,000 \times (1 + 0.0575 \times t) \]
In this case, \( t = 38 \):
\[ A = 10,000 \times (1 + 0.0575 \times 38) \]
First, calculate \( 0.0575 \times 38 \):
\[ 0.0575 \times 38 = 2.185 \]
Now, add 1 to this value:
\[ 1 + 2.185 = 3.185 \]
Now plug this value back into the formula:
\[ A = 10,000 \times 3.185 \]
Calculate \( A \):
\[ A = 31,850 \]
So, by the time you reach 65, you will have $31,850 in your retirement account with that interest rate using the provided formula.
Note: This formula calculates a simple interest scenario. In reality, most retirement accounts compound interest, and the future value (FV) would typically be calculated using the formula:
\[ FV = P \times (1 + r)^n \]
Where:
- \( P \) = initial principal balance (in this case, $10,000)
- \( r \) = annual interest rate (5.75% or 0.0575)
- \( n \) = number of years the money is invested (38 years)
Using this approach:
\[ FV = 10,000 \times (1 + 0.0575)^{38} \]
Calculating \( (1 + 0.0575)^{38} \):
\[ FV = 10,000 \times (1.0575)^{38} \approx 10,000 \times 5.89165 \approx 58,916.5 \]
So with compounding, the amount would be approximately $58,916.50.