To calculate the balance of a savings account with compounded interest, 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.
In this case:
- \( P = 30,000 \)
- \( r = 0.10 \) (10%)
- \( n = 10 \)
Substituting the values into the formula:
\[ A = 30000(1 + 0.10)^{10} \]
\[ A = 30000(1.10)^{10} \]
Calculating \( (1.10)^{10} \):
\[ (1.10)^{10} \approx 2.59374 \]
Now, multiply this by the principal:
\[ A \approx 30000 \times 2.59374 \approx 77712.20 \]
Thus, the balance after 10 years will be approximately $77,712.20.