Find the amount (integral value only) if a sum of ₹6,500 is borrowed at 10\% interest per annum for 2 years with interest compounded half-yearly.

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**Solution:**

1. Given principal $ P = 6500 $, annual interest rate $ R = 10\% $, time $ T = 2 $ years.

2. Since interest is compounded half-yearly, the rate per half year is:
   
   $$ R_{half} = \frac{10}{2} = 5\% $$

3. Number of compounding periods $ n = 2 \times 2 = 4 $ (because 2 years with 2 half-year periods per year).

4. The compound amount formula is:

$$ A = P \times \left(1 + \frac{R_{half}}{100}\right)^n $$

5. Substitute the values:

$$ A = 6500 \times \left(1 + \frac{5}{100}\right)^4 = 6500 \times (1.05)^4 $$

6. Calculate $ (1.05)^4 $:

$$ (1.05)^4 = 1.21550625 $$

7. Calculate the amount:

$$ A = 6500 \times 1.21550625 = 7890.29 $$

8. Taking the integral value, the amount is approximately ₹7,900.

**Answer:** ₹7,900

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