To calculate the balance after 6 years for a savings account with the formula \( A = P \left( 1 + \frac{r}{n} \right)^{nt} \), we will need to identify the values of \( P \), \( r \), \( n \), and \( t \) from your description.
Given:
- Principal \( P = 200 \)
- Interest rate \( r = 10% = 0.10 \)
- Compounding frequency \( n = 1 \) (since it's compounded annually)
- Time \( t = 6 \) years
Now we can substitute the values into the formula:
\[ A = 200 \left( 1 + \frac{0.10}{1} \right)^{1 \cdot 6} \]
Simplifying inside the parentheses:
\[ A = 200 \left( 1 + 0.10 \right)^{6} = 200 \left( 1.10 \right)^{6} \]
Now we need to calculate \( (1.10)^{6} \):
\[ (1.10)^{6} \approx 1.771561 \]
Now substituting back:
\[ A \approx 200 \times 1.771561 \approx 354.3122 \]
Rounding to the nearest cent:
\[ A \approx 354.31 \]
Thus, the balance after 6 years, rounded to the nearest cent, will be $354.31.