Use the compound interest formula to compute the balance in the following account after the stated period of​ time, assuming interest is compounded annually.
​$8000 invested at an APR of 3.9​% for 23 years.
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Part 1
The balance in the account after 23 years is ​$
  
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The compound interest formula is given by:

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

Where:
- $A$ is the amount of money (the balance) after interest,
- $P$ is the principal (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 or borrowed for, in years.

In this case:
- $P = 8000$,
- $r = 3.9\% = 0.039$,
- $n = 1$ (since it's compounded annually),
- $t = 23$ years.

Now we can calculate the balance:

\[
A = 8000 \left( 1 + \frac{0.039}{1} \right)^{1 \times 23}
\]

Let me calculate that for you.The balance in the account after 23 years will be approximately \$19,286.24.

Would you like any further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would the balance change if the interest were compounded monthly instead of annually?
2. What would the balance be if the investment period were extended to 30 years?
3. How does an APR of 5% over 23 years compare to the given 3.9%?
4. If \$10,000 were invested at the same rate, what would the balance be after 23 years?
5. How does compounding quarterly affect the balance compared to annual compounding?

**Tip:** When calculating interest, the frequency of compounding has a significant impact on the final amount. The more frequent the compounding, the higher the balance will grow.

Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually. ​$8000 invested at an APR of 3.9​% for 23 years.

Learn how to calculate compound interest with $8000 invested at an APR of 3.9% for 23 years. This detailed guide will walk you through the compound interest formula and provide the final balance after the investment period, highlighting key concepts like exponential growth and algebraic calculation. Suitable for high school students in Grades 10-12.

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