(a) Consider a bond with face value $100 and $5 annual coupons that matures in four years. Sketch the graph of the price of the bond as a function of the continuous compounding rate r. What is the value of this function for r = 0? What is the limit as r -> infinity?

(b) Consider a bond with face value $100 maturing in five years with coupons of $10 paid annually. Given the continuous compounding rate 12%, how long will it take for the price of the coupon bond to reach $95 for the first time?

(c) A bond with face value $100 and annual coupons $8 maturing after three years is redeemable at par. Find the corresponding continuous compounding rate assuming that the bond is purchased at par.