UPSC CDS II 2025 Mathematics Paper

Concept:The annual installment is calculated using the formula for present value of an annuity, where the loan amount equals the sum of discounted installments.Explanation:Given: Principal = ₹10,000, rate = 10% per annum ($r = 0.10$), time = 3 years, number of installments ($n$) = 3.The formula for each installment is: $\text{Installment} = \frac{P \times r}{1 - (1 + r)^{-n}}$.Substitute values: $\text{Installment} = \frac{10000 \times 0.10}{1 - (1.10)^{-3}}$.First, compute numerator: $10000 \times 0.10$ = ₹1000.Now, $(1.10)^{-3} = \frac{1}{(1.10)^3} = \frac{1}{1.331} \approx 0.7513$.Denominator: $1 - 0.7513 = 0.2487$.Thus, $\text{Installment} = \frac{1000}{0.2487} \approx \text{Rs. }4021$.Answer:The amount of each installment is approximately ₹4021, which corresponds to option (C).