Calculate, to the nearest cent, the future value *FV* (in dollars) of an investment of $10,000 at the stated interest rate after the stated amount of time.

2% per year, compounded annually, after 12 years

*FV* = $ 

The future value (FV) of an investment can be calculated using the formula for compound interest:

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

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

In this case:
- $ P = 10,000 $ dollars,
- $ r = 2\% = 0.02 $,
- $ n = 1 $ (compounded annually),
- $ t = 12 $ years.

Now, let's plug the values into the formula:

\[
FV = 10,000 \times \left(1 + \frac{0.02}{1}\right)^{1 \times 12}
\]

\[
FV = 10,000 \times (1.02)^{12}
\]

\[
FV = 10,000 \times 1.26824 = 12,682.43
\]

Thus, the future value is **$12,682.43**.

Would you like more details or explanations?

Here are 5 related questions you might find useful:
1. What would the future value be if the interest rate was 5% instead of 2%?
2. How does the formula change if the interest is compounded monthly instead of annually?
3. What would be the future value if the investment lasted for 20 years instead of 12?
4. How would the future value differ with a $20,000 initial investment?
5. What happens to the future value if no interest is compounded, but only simple interest is applied?

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

Calculate, to the nearest cent, the future value (FV) of an investment of $10,000 at the stated interest rate after the stated amount of time. 2% per year, compounded annually, after 12 years.

Learn how to calculate the future value of a $10,000 investment with 2% annual interest compounded annually for 12 years. This problem uses the compound interest formula to arrive at a future value of $12,682.43. Ideal for students in Grades 9-12 looking to understand exponential growth and investment concepts.

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