A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five years at a call price of $1,020. The bond currently sells for $1,059.34.

a) What are the yield to maturity and the yield to call of the bond?

b) What would be the yield to call annually if the call price were only $970?

c) What would be the yield to call annually if the call price were $1,020, but the bond could be called in two years instead of five years?

d) Sketch the price of the bond as a function of the interest rate.