Question: The yield to maturity (YTM) on zero-coupon 10-year corporate bond depends on the risk-free 1-year spot rate r and a risk parameter x according to the following formula: YTM=r+x+30rx. The YTM is expressed as annual rate with semi-annual compounding. Assume the face value of the bond is $10,000

a) (1 point) Find the bond price if r=0.08 (i.e., 6%) and x=0.02

b) (3 points) By how much the price of the bond will decrease if the risk parameter x increases by a small amount x. Write your answer as a linear function of x using linear approximation (Taylor series)

All interest rates are annual interest rates with semi-annual compounding unless specified otherwise. All coupon rates are annual coupon rates paid semi-annually unless specified otherwise.