1. **State the problem:** Calculate the Customer Lifetime Value (CLV) given quarterly spending of 1500, a gross margin of 25%, a customer duration of 3 years, and an annual discount rate of 10%. 2. **Identify variables:** - Quarterly spending, $S = 1500$ - Gross margin, $m = 0.25$ - Duration, $T = 3$ years - Annual discount rate, $r = 0.10$ - Number of quarters in 3 years, $n = 3 \times 4 = 12$ 3. **Calculate the margin per quarter:** $$\text{Margin per quarter} = S \times m = 1500 \times 0.25 = 375$$ 4. **Calculate the quarterly discount rate:** $$r_q = (1 + r)^{\frac{1}{4}} - 1 = (1 + 0.10)^{0.25} - 1 \approx 0.0241$$ 5. **Calculate the present value of the annuity (CLV):** The CLV is the sum of discounted margins over 12 quarters: $$\text{CLV} = \sum_{k=1}^{12} \frac{375}{(1 + r_q)^k}$$ This is a geometric series with first term $a = \frac{375}{1 + r_q}$ and ratio $\frac{1}{1 + r_q}$. 6. **Use the formula for the sum of a geometric series:** $$\text{CLV} = 375 \times \frac{1 - (1 + r_q)^{-12}}{r_q}$$ 7. **Calculate:** $$1 + r_q = 1.0241$$ $$ (1 + r_q)^{-12} = 1.0241^{-12} \approx 0.7513$$ $$\text{CLV} = 375 \times \frac{1 - 0.7513}{0.0241} = 375 \times \frac{0.2487}{0.0241} \approx 375 \times 10.32 = 3869.9$$ 8. **Final answer:** The approximate CLV is about 3870, closest to option ₹4,000. **Answer: ₹4,000**