please help solve using excel and show formulas thank you!

A $500 million bond portfolio currently has a modified duration of 12.5 years. The portfolio manager wishes to reduce the modified duration to 8.0 by using a futures contract priced at $105,250. The futures contract has an implied modified duration of 9.25 . The portfolio manager has estimated that the yield on the bond portfolio is about 8% more volatile than the implied yield on the futures contract. A. Indicate whether the portfolio manager should enter a short or long futures position. B. Calculate the number of contracts needed to change the duration of the bond portfolio. C. Assume that on the horizon date, the yield on the bond portfolio has declined by 50 basis points and the portfolio value has increased by $31,343,750. The implied yield on futures has decreased by 46 basis points, and the futures contract is priced at $109,742. Calculate the overall gain on the position, bond \& futures. Determine the ex-post duration with and without the futures transaction. A $500 million bond portfolio currently has a modified duration of 12.5 years. The portfolio manager wishes to reduce the modified duration to 8.0 by using a futures contract priced at $105,250. The futures contract has an implied modified duration of 9.25 . The portfolio manager has estimated that the yield on the bond portfolio is about 8% more volatile than the implied yield on the futures contract. A. Indicate whether the portfolio manager should enter a short or long futures position. B. Calculate the number of contracts needed to change the duration of the bond portfolio. C. Assume that on the horizon date, the yield on the bond portfolio has declined by 50 basis points and the portfolio value has increased by $31,343,750. The implied yield on futures has decreased by 46 basis points, and the futures contract is priced at $109,742. Calculate the overall gain on the position, bond \& futures. Determine the ex-post duration with and without the futures transaction