Rajnish borrowed ₹1,500 from a bank and repaid the entire amount with interest in two equal annual installments, the first installment being paid a year after Rajnish borrowed from the bank. If the rate of interest was 40\% per annum, compounded annually, then what was the value (in ₹) of each installment paid by Rajnish?

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**Solution:**

1. Let the principal amount be $ P = 1500 $, rate of interest $ R = 40\% $, and each equal annual installment be $ x $.

2. The present value of the first installment paid after 1 year is:
   $$
   \frac{x}{(1 + R/100)^1} = \frac{x}{1.4}
   $$

3. The present value of the second installment paid after 2 years is:
   $$
   \frac{x}{(1 + R/100)^2} = \frac{x}{(1.4)^2} = \frac{x}{1.96}
   $$

4. The sum of the present values of both installments equals the principal:
   $$
   1500 = \frac{x}{1.4} + \frac{x}{1.96}
   $$

5. Combine the terms:
   $$
   1500 = x \left( \frac{1}{1.4} + \frac{1}{1.96} \right) = x \left( \frac{1.96 + 1.4}{1.4 \times 1.96} \right) = x \times \frac{3.36}{2.744}
   $$

6. Calculate the fraction:
   $$
   \frac{3.36}{2.744} \approx 1.224489
   $$

7. Solve for $ x $:
   $$
   x = \frac{1500}{1.224489} \approx 1225
   $$

**Answer:** The value of each installment is ₹1225.

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