You invest 32,000 into a bank account that earns 2.64% APR, compounded monthly, for 20 years. Round the result to the nearest penny.

To calculate the future value of an investment compounded monthly, we use the compound interest formula:

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

Where:
- $ A $ is the amount of money accumulated after n years, including interest.
- $ P $ is the principal amount (the initial money), which is \$32,000.
- $ r $ is the annual interest rate (decimal), so $ r = \frac{2.64}{100} = 0.0264 $.
- $ n $ is the number of times the interest is compounded per year (monthly, so $ n = 12 $).
- $ t $ is the time the money is invested for, in years (20 years).

Now, we plug in the values:

\[
A = 32000 \left(1 + \frac{0.0264}{12}\right)^{12 \times 20}
\]

Let me calculate the result for you.The future value of the investment after 20 years, compounded monthly at an annual interest rate of 2.64%, is approximately **\$54,225.75**.

Would you like further clarification or details on any part of the calculation?

Here are 5 related questions to explore further:
1. What would happen if the interest were compounded quarterly instead of monthly?
2. How much interest is earned over the 20 years?
3. What if you invested \$32,000 at a higher interest rate, such as 3.5% APR, compounded monthly?
4. How would the future value change if the investment period was extended to 30 years?
5. How does continuous compounding affect the future value compared to monthly compounding?

**Tip:** Increasing the frequency of compounding (e.g., from monthly to daily) will slightly increase the future value due to more frequent application of interest.

Learn how to calculate the future value of a $32,000 investment with an APR of 2.64%, compounded monthly over 20 years. This problem involves key algebraic concepts, including the compound interest formula, and is suitable for students in Grades 10-12.

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