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\mathrm{.}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.