Use the compound interest formula to compute the balance in the following account after the stated period of​ time, assuming interest is compounded annually.
​$15 comma 000 invested at an APR of 3.9​% for 17 years.

The compound interest formula is given by:

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

Where:
- $A$ is the final amount (balance after the interest period),
- $P$ is the principal amount (initial investment),
- $r$ is the annual interest rate (as a decimal),
- $n$ is the number of times the interest is compounded per year,
- $t$ is the time the money is invested for (in years).

For this problem:
- $P = 15,000$,
- $r = 3.9\% = 0.039$,
- $n = 1$ (since the interest is compounded annually),
- $t = 17$ years.

Now we can plug these values into the formula:

\[
A = 15,000 \left(1 + \frac{0.039}{1}\right)^{1 \times 17}
\]

\[
A = 15,000 \left(1 + 0.039\right)^{17}
\]

\[
A = 15,000 \left(1.039\right)^{17}
\]

Now I'll calculate the balance $A$.The balance in the account after 17 years, with an APR of 3.9% compounded annually, will be approximately $28,744.55.

Would you like further clarification or details on how this was calculated?

Here are 5 related questions you might find helpful:
1. What would the balance be if the interest were compounded monthly?
2. How does increasing the APR affect the final balance?
3. How would the formula change if interest were compounded quarterly?
4. What happens to the final amount if the investment period is shortened to 10 years?
5. How do continuous compounding and annual compounding compare?

**Tip:** The more frequently interest is compounded, the more interest accumulates over time!

Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. $15,000 invested at an APR of 3.9% for 17 years.

Learn how to calculate the final balance of $15,000 invested at an APR of 3.9% for 17 years using the compound interest formula. This step-by-step solution includes key mathematical concepts like exponential growth and compound interest, ideal for high school students in Grades 10-12.

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