Show your work step by step: For calculation questions, you do not have to copy the formula; however, you must show how you substitute the numbers into the formula. For example, to calculate future value, an appropriate answer is: Face value = 100*e^(0.1*1) = 110.5157. An answer of 110.5157 without showing the working process will be penalized.

Keep 4 decimal points.

Consider a long forward contract to purchase a coupon-bearing bond, expiring in 12 months. The current price of the bond is $1000. A coupon payment of $40 is expected after 3 months, and $50 is expected after 6 months. The risk-free rate is 5% per annum with continuous compounding for all maturities. (Required: Show your work step by step)

(a) What is the theoretical forward price?

(b) Is there an arbitrage opportunity if the real forward price is $900? If yes, explain how to generate the arbitrage profit step by step and calculate the arbitrage profit. If not, explain why there is not such an opportunity.