PART A: Suppose a one-year zero-coupon bond with a face value of $1,000 is sold at $980, a two-year zero-coupon bond is sold at $950, and a three-year zero-coupon bond is sold at $920. (a) Calculate the 1-year, 2-year and 3-year spot rates. (Show your workings to 4 places for a percentage - e,g. 0.1234%. Assume annual compounding) (b) Assuming you wish to purchase a 3-year 5% annual coupon bond: Based on the spot rates calculated in part (a), and the cash flows relating to this bond, calculate the price of a 3-year 5% annual coupon bond. (c) Prove that the Yield-to-Maturity of this Bond is 2.8% PART B: Describe the relationship between an increase in interest rates, the price of a bond and: i. the size of coupon payments (i.e. if interest rates increase, how will the price of a bond move if it has large coupons vs if it has small coupons) ii. the time to maturity of the bond (i.e. if interest rates increase, how will the price of a bond move if it has a long time to maturity vs if it has a short time to maturity) iii. the market level of interest rates (i.e. if interest rates increase, how will the price of a bond move if market interest rates are low vs if market interest rates are high)