2900 dollars is placed in an account with an annual interest rate of 9%. How much will be in the account after 13 years, to the nearest cent?

To find out how much money will be in the account after 13 years, we will use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]

Where:
- $ A $ is the amount in the account after time $ t $,
- $ P $ is the principal (initial amount), which is \$2900,
- $ r $ is the annual interest rate (9% or 0.09),
- $ t $ is the time in years (13 years),
- $ n $ is the number of times the interest is compounded per year. If not specified, we'll assume it's compounded annually, so $ n = 1 $.

Substituting the given values into the formula:

\[
A = 2900 \left(1 + \frac{0.09}{1}\right)^{1 \times 13}
\]

\[
A = 2900 \left(1.09\right)^{13}
\]

Now we compute:

\[
A = 2900 \times 3.138429
\]

\[
A \approx 9101.44
\]

So, the amount in the account after 13 years, to the nearest cent, is **\$9101.44**.

Would you like further details, or do you have any questions?

Here are five related questions to explore:
1. How would the amount change if the interest were compounded quarterly?
2. What if the interest rate was 12% instead of 9%?
3. How much interest is earned over the 13 years?
4. How would the formula change for continuous compounding?
5. What is the future value if \$2900 is compounded monthly?

**Tip:** Always clarify how often the interest is compounded, as this impacts the final amount significantly!

Find out how much $2900 will grow to after 13 years at an annual interest rate of 9%, using the compound interest formula. Learn the key concepts of exponential growth and compound interest. Perfect for high school students studying finance and algebra.

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