1. **Problem Statement:** Calculate the settlement payment of a Forward Rate Agreement (FRA) that covers 9 months starting in 6 months, with a notional principal of 15 crore, an agreed rate of 7.5%, current 9-month LIBOR at 7%, and a discount factor for 9 months of 0.965. 2. **Formula Used:** The settlement payment for an FRA is calculated as: $$\text{Settlement Payment} = \frac{\text{Notional} \times (R_{agreed} - R_{LIBOR}) \times T}{1 + R_{LIBOR} \times T}$$ where $R_{agreed}$ is the agreed rate, $R_{LIBOR}$ is the current LIBOR rate, and $T$ is the FRA period in years. 3. **Important Notes:** - The period $T$ is 9 months, which is $\frac{9}{12} = 0.75$ years. - The payment is discounted using the discount factor for 9 months, which is 0.965. 4. **Calculate the numerator:** $$15,00,00,000 \times (0.075 - 0.07) \times 0.75 = 15,00,00,000 \times 0.005 \times 0.75 = 56,25,000$$ 5. **Calculate the denominator:** $$1 + 0.07 \times 0.75 = 1 + 0.0525 = 1.0525$$ 6. **Calculate the settlement payment before discounting:** $$\frac{56,25,000}{1.0525} \approx 53,45,454.55$$ 7. **Apply the discount factor:** $$53,45,454.55 \times 0.965 \approx 51,58,636.36$$ 8. **Interpretation:** Since the agreed rate is higher than the LIBOR, the seller pays the buyer. The payment is approximately ₹51.59 lakh. 9. **Check options:** None of the options exactly match ₹51.59 lakh, but the closest is option (a) ₹29.4 lakh paid by seller or (b) ₹29.4 lakh received by buyer. Since our calculation is higher, re-checking the problem shows the discount factor is already applied in the denominator, so we should not multiply again. 10. **Recalculate without discount factor multiplication:** Settlement payment = $\frac{15,00,00,000 \times (0.075 - 0.07) \times 0.75}{1 + 0.07 \times 0.75} = 53,45,454.55$ approx ₹53.45 lakh. 11. **Discount factor is used to find present value, so the actual settlement payment is:** $$53,45,454.55 \times 0.965 = 51,58,636.36$$ 12. **Since the problem states discount factor for 9 months is 0.965, the payment is discounted to present value, so the payment is ₹51.59 lakh paid by seller.** 13. **None of the options match exactly, but the closest is option (a) ₹29.4 lakh paid by seller, which might be a typographical error or different assumptions.** **Final answer:** Approximately ₹51.59 lakh paid by seller.