To calculate the total amount of money you will pay back on a loan with simple interest, you can use the formula:
\[ A = P(1 + rt) \]
where:
- \( A \) is the total amount paid back,
- \( P \) is the principal amount (the initial amount borrowed),
- \( r \) is the annual interest rate (in decimal form), and
- \( t \) is the time (in years).
In your case:
- \( P = 2300 \),
- \( r = 0.06 \) (since 6% expressed as a decimal is 0.06),
- \( t = 9 \).
Now, substituting the values into the formula:
\[ A = 2300(1 + (0.06 \times 9)) \]
Calculating \( 0.06 \times 9 \):
\[ 0.06 \times 9 = 0.54 \]
Now, add 1 to that result:
\[ 1 + 0.54 = 1.54 \]
Now, multiply by the principal:
\[ A = 2300 \times 1.54 = 3542 \]
Thus, the total amount of money you will pay back after 9 years is $3,542.