Hugh has invested $25,000
 in an account that will pay compound interest every month, at the annual percentage rate of interest of 3.84%
.

a.
Use the compound interest rule to determine the balance of Hugh’s investment after three years.



To calculate the balance of Hugh’s investment after 3 years with compound interest, we use the compound interest formula:

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

Where:
- $ A $ is the final amount (balance).
- $ P = 25,000 $ is the principal (initial investment).
- $ r = 3.84\% = 0.0384 $ is the annual interest rate.
- $ n = 12 $ is the number of times the interest is compounded per year (monthly).
- $ t = 3 $ is the time in years.

Now, substitute the values into the formula:

\[
A = 25,000 \left(1 + \frac{0.0384}{12}\right)^{12 \times 3}
\]

Let's calculate the balance.The balance of Hugh's investment after 3 years will be approximately **$28,047.29**.

Would you like further details or have any questions? Here are some related questions to expand your understanding:

1. How does increasing the interest rate affect the final amount?
2. What happens if the compounding frequency is changed to quarterly?
3. How would the balance change if the investment duration was extended to 5 years?
4. What is the difference between simple and compound interest?
5. How can continuous compounding be applied to this problem?

**Tip:** The more frequently interest is compounded, the larger the final amount due to more frequent application of interest on the balance.

Hugh has invested $25,000 in an account that will pay compound interest every month, at the annual percentage rate of interest of 3.84%. Use the compound interest rule to determine the balance of Hugh’s investment after three years.

Determine the final balance of Hugh's $25,000 investment over 3 years using monthly compounding at an annual interest rate of 3.84%. This example explains compound interest and exponential growth, ideal for students in Grades 10-12.

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