To calculate the balance of an investment that is compounded annually, you can 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 for.
In this case:
- \( P = 10,000 \)
- \( r = 0.05 \) (5% as a decimal)
- \( n = 6 \)
Now plug the values into the formula:
\[ A = 10,000(1 + 0.05)^6 \]
Calculate \( (1 + 0.05)^6 \):
\[ (1.05)^6 \approx 1.340095 \]
Now calculate \( A \):
\[ A \approx 10,000 \times 1.340095 \approx 13,400.95 \]
So, the balance after 6 years will be approximately:
\[ \text{The account balance will be } \mathbf{13,400.95} \]
(Rounded to the nearest cent as needed.)