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To calculate the future value $ FV $ of an investment using annual compounding, we can use the formula:

\[
FV = P \times (1 + r)^t
\]

where:
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (expressed as a decimal),
- $ t $ is the time in years.

From the problem:
- $ P = 10,000 $,
- $ r = 1\% = 0.01 $,
- $ t = 14 $ years.

Plugging in the values:

\[
FV = 10,000 \times (1 + 0.01)^{14}
\]

Calculating step-by-step:

1. $ 1 + 0.01 = 1.01 $,
2. $ 1.01^{14} \approx 1.149 $ (rounded to three decimal places),
3. $ 10,000 \times 1.149 = 11,490 $.

Thus, the future value $ FV $ is approximately:

\[
FV = 11,490
\]

So, the answer to the nearest cent is **$11,490.00**.

Would you like further details on each calculation step or have any questions?

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Here are some follow-up questions related to this topic:
1. How would the future value change if the interest rate were compounded quarterly?
2. What would the future value be if the investment period was 10 years instead of 14 years?
3. How does changing the interest rate to 2% per year affect the future value?
4. What formula would be used if the compounding were continuous instead of annual?
5. How does inflation affect the real future value of investments?

**Tip:** When compounding more frequently than annually, the effective interest rate is slightly higher, leading to a greater future value.

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: 1% per year, compounded annually, after 14 years.

Learn how to calculate the future value of an investment of $10,000 at a 1% annual interest rate, compounded annually, after 14 years. This problem involves using the compound interest formula and is ideal for high school students (Grades 10-12) studying exponential growth.

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