Anil invests Rs. 22000 for 6 years in a certain scheme with 4% interest per annum, compounded half-yearly.

To calculate the future value of Anil's investment, we use the compound interest formula:

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

Where:
- \(A\) is the amount of money after interest.
- \(P\) is the principal (initial investment) = Rs. 22,000.
- \(r\) is the annual interest rate = 4% (expressed as 0.04).
- \(n\) is the number of times the interest is compounded per year = 2 (since it's compounded half-yearly).
- \(t\) is the number of years = 6.

Now, let's plug in the values and calculate the amount:

\[
A = 22000 \left( 1 + \frac{0.04}{2} \right)^{2 \times 6}
\]
\[
A = 22000 \left( 1 + 0.02 \right)^{12}
\]
\[
A = 22000 \left( 1.02 \right)^{12}
\]

Next, we calculate \(1.02^{12}\) and then multiply it by 22,000 to find the final amount \(A\).

Let me compute that for you.The final amount Anil will have after 6 years, with 4% interest compounded half-yearly, is approximately **Rs. 27,901.32**.

Would you like to see further details or have any questions about this?

Here are five related questions for further exploration:
1. What if the interest rate was 5% instead of 4%?
2. How much interest does Anil earn in total over 6 years?
3. How would the amount change if the interest was compounded quarterly instead of half-yearly?
4. What would be the future value if Anil invested Rs. 30,000 instead of Rs. 22,000?
5. How does the time of investment (e.g., 10 years instead of 6) affect the final amount?

**Tip:** The more frequently interest is compounded, the higher the final amount becomes!

Calculate the future value of Rs. 22000 invested for 6 years with a 4% annual interest rate compounded half-yearly. This problem uses the compound interest formula and explores concepts like exponential growth and interest compounding. Suitable for Grades 9-12.

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