A 4-year zero coupon bond has a face value of $100 and a price of $82.270. The table below contains prices, coupons and the time to maturity for 3 annual coupon paying bonds that have a face value of $100. Please use annual compounding and annual discounting in your calculations and 3 decimal places in your workings

Time to Maturity (Years) Annual Coupon Price 1 3.0% $98.095 2 6.5% $102.790 3 5.8% $102.179

a) What is the price of a 3-year bond paying annual coupons of 5% and a face value of $100?

b) If you had $1 million invested in the 3-year 5% coupon bond, how many of the 4-year zerocoupon bonds would you need to short-sell to hedge your interest rate risk?

c) Without doing any calculations, discuss what actions you would need to take with your short position in the zero coupon to ensure your interest rate risk remained hedged until the maturity of the 3-year coupon paying bond.