Consider a 9-month forward contract to purchase a coupon-bearing bond whose current price is $900. A coupon payment of $40 is expected on the bond after 4 months. Assume that the 4-month and 9-month risk-free rates (continuously compounded) are, respectively, 3% and 4% per annum.

(a) Compute the arbitrage-free forward price.

(b) Argue that if the forward price is at $910 then there exists an arbitrage opportunity.

(c) Argue that if the forward price is at $870 then there exists an arbitrage opportunity.