To represent the total amount of money \( A \) in your retirement account after \( t \) years with an initial investment of $10,000 and an annual interest rate of 5.75%, you would use the formula for compound interest.
The general formula for compound interest is:
\[ A = P(1 + r)^t \]
where:
- \( A \) is the total amount of money after \( t \) years,
- \( P \) is the principal amount (the initial investment),
- \( r \) is the annual interest rate (as a decimal), and
- \( t \) is the number of years the money is invested or borrowed.
In your case:
- \( P = 10,000 \)
- \( r = 5.75% = 0.0575 \)
Using these values, the equation can be written as:
\[ A = 10,000(1 + 0.0575)^t \]
So, filling in the blanks provided, the equation will be:
\[ A = 10,000 \times (1 + 0.0575)^t \]
This is the correct representation of the total amount of money in your account after \( t \) years.