the initial value of an investment is $**15,000. If the investment earns an annual interest of 1.1%, what is its value in 8 years?**

To calculate the future value of an investment with annual compound interest, we use the 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 amount of money), which is $15,000 in this case.
- $r$ is the annual interest rate (decimal), which is 1.1%, or 0.011 as a decimal.
- $n$ is the number of times that interest is compounded per year. If it's compounded annually, $n = 1$.
- $t$ is the time the money is invested for, which is 8 years in this case.

Given that the interest is compounded annually ($n = 1$), the formula simplifies to:

\[
A = P \left(1 + r\right)^t
\]

Let's substitute the given values into the formula:

\[
A = 15000 \left(1 + 0.011\right)^8
\]

\[
A = 15000 \left(1.011\right)^8
\]

Now we calculate $ \left(1.011\right)^8 $:

\[
(1.011)^8 \approx 1.092727
\]

So,

\[
A \approx 15000 \times 1.092727
\]

\[
A \approx 16390.91
\]

Therefore, the value of the investment after 8 years is approximately $16,390.91.

Would you like more details or have any questions?

Here are some related questions to expand on this topic:
1. How would the future value change if the annual interest rate was 2%?
2. What is the formula for continuous compound interest?
3. How do you calculate the total interest earned over the 8-year period?
4. What would be the future value if the investment was compounded quarterly instead of annually?
5. How do changes in the principal amount affect the future value of an investment?
6. How does the duration of the investment impact the future value?
7. What is the difference between simple interest and compound interest?
8. How can you calculate the future value of an investment with varying annual interest rates?

**Tip:** Always ensure you convert percentage rates to decimal form before using them in calculations by dividing the percentage by 100.

Learn how to calculate the future value of a $15,000 investment with an annual interest rate of 1.1% over 8 years using compound interest formula. Understand the step-by-step process and formula application. Suitable for high school students and anyone interested in financial mathematics.

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