It is a $20-$year, $10\%$ coupon bond that coupons are paid annually. Par value is $$1,000$ and the current required yield is $8\%.$ At the end of year $5,$ the yield will be either $4\%$ with $40\%$ probability or $12\%.$

a$)$ What is the bond price?

b$)$ The bond will be called at par value plus two coupon payments if the bond price is higher than the call price. What is the bond price?

c$)$ The bond will be called at par value plus two coupon payments if the bond price is higher than the call price. What must the coupon rate be if the bond price is $$1,170\mathrm{.}16?$

d$)$ The bond will be called at the PV $($discounted at $3\%)$ of remaining cash flows if the yield is $4\%.$ What is the bond price?