You hold a $50 million portfolio of par value bonds with a coupon rate of 10 percent paid annually and 15 years to maturity. How many T-bond futures contracts do you need to hedge the portfolio against an unanticipated change in the interest rate of 0.18%? Assume the market interest rate is 10 percent and that T-bond futures contracts call for delivery of an 8 percent coupon (paid annually), 20-year maturity T-bond.

A.398 contracts long

B.524 contracts short

C.1048 contracts short

D.398 contracts short

Please provide thorough (step-by-step) solution and specify how each values are obtained. Thank you