To find the balance after 10 years for an investment of $25,000 at an interest rate of 5% 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.
Given:
- \( P = 25,000 \)
- \( r = 0.05 \) (5% as a decimal)
- \( n = 10 \)
Now, plug the values into the formula:
\[ A = 25000 \times (1 + 0.05)^{10} \] \[ A = 25000 \times (1.05)^{10} \] \[ A = 25000 \times 1.628894626777442 \] (approximately) \[ A \approx 40722.36 \]
So, the account balance after 10 years will be approximately $40,722.36.
Rounding to the nearest cent, the answer is:
$40,722.36.