Question

Erica opened the savings account and deposited $200 as principal the account earns 10% interest compounded annually what is the balance after 6 years use the formula equals p * 1 + r / n to the power of NT where a is the balance p is the principal r is the interest rate represented as a decimal n is the number of times per year that the interest is compounded and t is the time of years round your answer to the nearest cent

Answer 1

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**.