A $20-$year maturity bond with par value of $$1,000$ makes semiannual coupon payments at a coupon rate of $8\%.$ Find the bond equivalent and effective annual yield to maturity of the bond if the bond price is:

a$.$ $$950$

b$.$ $$1,000$

c$.$ $$1,050$

Repeat Problem $11$ using the same data, but now assume that the bond makes its coupon payments annually. Why are the yields you compute lower in this case? Solve ex $12.$