To find the balance of the investment account after 13 years, you will need to use the formula for compound interest:
\[ A = P (1 + r)^n \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.
From your description:
- The principal \( P = 275 \)
- The annual interest rate \( r = 3.2% = 0.032 \)
- The number of years \( n = 13 \)
Substituting these values into the formula:
\[ A = 275 (1 + 0.032)^{13} \]
Calculating \( (1 + 0.032)^{13} \):
\[ 1 + 0.032 = 1.032 \]
Now raise \( 1.032 \) to the power of \( 13 \):
\[ 1.032^{13} \approx 1.487 \] (rounded to three decimal places for simplicity; you can use a calculator for precise value).
Now substitute back into the formula:
\[ A \approx 275 \times 1.487 \approx 409.925 \]
Therefore, the balance of the account after 13 years is approximately $409.93.