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The problem provided has the following details:

- **Principal (P)** = ₹20,000
- **Time (T)** = 1 year
- **Rate (R)** = 12% per annum
- **Interest compounded half-yearly**

To solve for the amount and the compound interest when the interest is compounded half-yearly, we use the formula:

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

Where:
- \( A \) = Final amount
- \( P \) = Principal
- \( r \) = Annual interest rate (in decimal)
- \( n \) = Number of times the interest is compounded per year
- \( t \) = Time in years

In this case:
- \( P = 20,000 \)
- \( r = \frac{12}{100} = 0.12 \)
- \( n = 2 \) (since the interest is compounded half-yearly)
- \( t = 1 \) year

Now, let me calculate the final amount \( A \) and the compound interest.

The final amount \( A \) after 1 year, with interest compounded half-yearly, is ₹22,472.

The compound interest earned over the year is ₹2,472.

Would you like more details or have any questions?

Here are 8 related questions to expand on this topic:
1. What if the interest were compounded quarterly instead of half-yearly?
2. How does the compound interest formula change with different compounding periods?
3. Can you calculate simple interest for the same scenario?
4. How does the final amount change if the rate is increased to 15% per annum?
5. What if the principal was ₹50,000 instead of ₹20,000?
6. How would the result differ if the time was 2 years instead of 1 year?
7. Can you explain the difference between compound and simple interest in detail?
8. How does the frequency of compounding affect the amount of interest earned?

**Tip:** Compounding more frequently generally results in higher interest earnings due to interest being applied to the accumulated interest more often.

Learn how to calculate compound interest with half-yearly compounding using the compound interest formula. This problem involves a principal of ₹20,000, an annual interest rate of 12%, and a time period of 1 year. Understand how compounding frequency affects the final amount and compound interest earned.

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