(a) (8 points) Find the price of a 10% Government coupon bond that pays annual coupons, matures in exactly 2 years, and has a face value of $1,000. The APR is 4% p.a. compounded annually. The bond has just paid its annual coupon, hence you need to price it assuming that the first coupon that you will receive is due in exactly one year. (b) (7 points) In addition to the 10% coupon bond you observe two more zero coupon bonds which will mature in 1 and 2 years from now, both with a face value of $100. The prices of these bonds are given below: Time to Maturity (years) Face value Price 1 $100 $96.15 2 $100 $82.17 Are the prices of these two zero coupon bonds consistent with the price of the 10% coupon bond that you solved for in part (a)? If the prices are inconsistent show, in detail, using an arbitrage table, how you can make risk-less arbitrage profits. Does your arbitrage profit depend on the possibility that the APR will change in one year? You are allowed to both buy or sell the coupon bond and any of the zero-coupon bonds.