Question

Erica opened a savings account and deposited $200.00 as principal. The account earns 10% interest, compounded annually. What is the balance after 6 years?
Use the formula A=P(1+ r/n)^nt , where A is the balance (final amount), P is the principal (starting amount), r is the interest rate expressed as a decimal, n is the number of times per year that the interest is compounded, and t is the time in years.
Round your answer to the nearest cent.
$

Answer 1

To calculate the balance after 6 years for Erica's savings account using the formula \( A = P(1 + \frac{r}{n})^{nt} \), we can plug in the given values:

- \( P = 200.00 \) (the principal)
- \( r = 0.10 \) (the annual interest rate expressed as a decimal)
- \( n = 1 \) (the interest is compounded annually)
- \( t = 6 \) (the time in years)

Now we can substitute these values into the formula:

\[
A = 200(1 + \frac{0.10}{1})^{1 \times 6}
\]

This simplifies to:

\[
A = 200(1 + 0.10)^{6}
\]
\[
A = 200(1.10)^{6}
\]

Next, we calculate \( (1.10)^{6} \):

\[
(1.10)^6 \approx 1.771561
\]

Now substitute this value back into the equation for \( A \):

\[
A \approx 200 \times 1.771561
\]

Calculating this gives:

\[
A \approx 354.3122
\]

Finally, rounding to the nearest cent, we find:

\[
A \approx 354.31
\]

Thus, the balance after 6 years will be **$354.31**.