An investment of k2,200 is made at an annual interest rate of 12%. What is the compound interest after 5 years?

To calculate the compound interest, we use the formula:

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

Where:
- \(A\) is the amount of money after interest
- \(P\) is the principal amount (initial investment)
- \(r\) is the annual interest rate (decimal form)
- \(n\) is the number of times interest is compounded per year
- \(t\) is the number of years

In this case:
- \(P = k2,200\)
- \(r = 12\% = 0.12\)
- \(n = 1\) (since it's compounded annually)
- \(t = 5\) years

First, let's calculate \(A\), and then subtract the principal \(P\) to get the compound interest.

\[
A = 2200 \left(1 + \frac{0.12}{1}\right)^{1 \times 5} = 2200 \times (1.12)^5
\]

Now, let's compute the final value.The total amount after 5 years is approximately \( k3,877.15 \). 

To find the compound interest, we subtract the initial investment from this total:

\[
\text{Compound Interest} = A - P = k3,877.15 - k2,200 = k1,677.15
\]

So, the compound interest after 5 years is approximately **k1,677.15**.

Would you like more details or have any questions about the calculation?

Here are 5 related questions for further exploration:
1. What would the compound interest be if the rate were 15% instead of 12%?
2. How does the interest change if compounded semi-annually instead of annually?
3. How would the interest differ with an investment duration of 10 years instead of 5 years?
4. What is the formula for continuously compounded interest, and how would it apply here?
5. What would be the compound interest if the initial investment were doubled?

**Tip:** Always convert percentage rates to their decimal form when using them in formulas (e.g., 12% becomes 0.12).

Learn how to calculate compound interest for an investment of k2,200 at an annual interest rate of 12% over 5 years. Using the compound interest formula, this solution provides a detailed step-by-step explanation. Suitable for students in Grades 9-12.

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