Consider a 6-month forward contract on a zero-coupon bond with a face value of $4,000 that is currently priced at $3,800, and suppose that the annual risk-free rate is 10%.

(a) Determine the arbitrage-free forward price, assuming continuous compounding.

(b) Suppose the forward price in the contract is actually $4100 rather than the no-arbitrage price your calculated in part (a). How to arbitrage? (Please write clearly what you need to do today and what happens at the settlement date.) What is the risk-free profit?

(c) Suppose the forward/futures price in the contract is actually $3900 rather than the no-arbitrage price your calculated in part (a). How to arbitrage? (Please write clearly what you need to do today and what happens at the settlement date.) What is the risk-free profit?