What is the future value of $100 after 3 years if the appropriate interest rate is 8% compounded monthly?

To find the future value $ FV $ of an investment compounded monthly, we use the formula:

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

Where:
- $ P $ is the principal amount (initial investment).
- $ r $ is the annual interest rate (decimal).
- $ n $ is the number of times the interest is compounded per year.
- $ t $ is the time in years.

Given:
- $ P = 100 $
- $ r = 0.08 $ (8% annual interest rate)
- $ n = 12 $ (compounded monthly)
- $ t = 3 $ years

Substituting these values into the formula:

\[
FV = 100 \left(1 + \frac{0.08}{12}\right)^{12 \times 3}
\]

Let's calculate:

1. **Calculate the monthly interest rate:** $ \frac{0.08}{12} = 0.00667 $.
2. **Calculate the number of total compounding periods:** $ 12 \times 3 = 36 $.
3. **Compute the compound factor:** $ \left(1 + 0.00667\right)^{36} \approx 1.26824 $.
4. **Find the future value:** $ 100 \times 1.26824 \approx 126.82 $.

The future value of $100 after 3 years at an 8% interest rate compounded monthly is approximately **$126.82**.

Would you like more details or have any questions?

Here are some related questions:
1. What is the future value if the interest rate changes to 6%?
2. How does compounding quarterly compare to compounding monthly?
3. What would be the future value if compounded annually?
4. How does increasing the number of years affect the future value?
5. What is the present value needed to reach $200 in 3 years at 8% compounded monthly?

**Tip:** The more frequently interest is compounded, the higher the future value will be due to the effect of compounding more often.

Calculate the future value of $100 after 3 years with an 8% annual interest rate compounded monthly. This problem uses the compound interest formula and covers key concepts like exponential growth and interest compounding. Ideal for students in Grades 10-12.

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