3. The zero-coupon bond maturing in 18 months has face value $1,000. The yield curve is flat at 5% (quoted as a continuously compounded APR). The 12-month forward price prevailing in the market for this zero-coupon bond is $1,010.

(a) Is there an arbitrage opportunity in the market? If so, describe the arbitrage portfolio and resulting cash flows.

(b)What is the arbitrage-free twelve-month forward price for this 18-month treasury bond?