To calculate the balance after 6 years for Erica's savings account, we can use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the balance after time \( t \),
- \( P \) is the principal amount (the initial deposit),
- \( r \) is the annual interest rate (as a decimal),
- \( n \) is the number of times interest is compounded per year,
- \( t \) is the number of years.
Given the information:
- \( P = 200.00 \)
- \( r = 10% = 0.10 \)
- \( n = 1 \) (interest is compounded annually)
- \( t = 6 \)
Now we can substitute these values into the formula:
\[ A = 200 \left(1 + \frac{0.10}{1}\right)^{1 \times 6} \]
This simplifies to:
\[ A = 200 \left(1 + 0.10\right)^{6} = 200 \left(1.10\right)^{6} \]
Next, we calculate \( (1.10)^{6} \):
\[ (1.10)^{6} \approx 1.771561 \]
Now multiply this by the principal:
\[ A \approx 200 \times 1.771561 \approx 354.3122 \]
Finally, rounding to the nearest cent, the balance after 6 years will be:
\[ \boxed{354.31} \]
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