Calculate the value in 3 years of an investment of $5,000 earning 5% pa compound interest.

To calculate the value of an investment after 3 years with compound interest, we can 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 investment), which is $5,000.
- $r$ is the annual interest rate (in decimal), which is 5%, or 0.05.
- $n$ is the number of times that interest is compounded per year. Since it's compounded annually, $n = 1$.
- $t$ is the number of years the money is invested, which is 3 years.

Now, plug the values into the formula:

\[
A = 5000 \left(1 + \frac{0.05}{1}\right)^{1 \times 3}
\]

\[
A = 5000 \left(1 + 0.05\right)^3
\]

\[
A = 5000 \times 1.157625
\]

\[
A = 5788.125
\]

So, the value of the investment after 3 years is **$5,788.13**.

Would you like details or have any questions?

Here are some related questions:
1. What would the amount be after 5 years instead of 3?
2. How does the value change if the interest is compounded semi-annually instead of annually?
3. What is the difference between simple and compound interest?
4. How would the final amount differ with a 7% interest rate instead of 5%?
5. What would the investment grow to after 10 years with the same conditions?
6. What if the interest was compounded monthly? What would the final value be?
7. How is the compound interest formula derived?
8. What is the effect of continuous compounding on the final amount?

**Tip:** The more frequently interest is compounded, the greater the amount of interest earned.

Calculate the future value of a $5,000 investment earning 5% annual compound interest over 3 years. Understand the compound interest formula and step-by-step calculation. Suitable for Grades 9-12.

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