Bond X pays a $9\%$ semiannual coupon, has a YTM of $6\%$ and has $12$ years to maturity.

Bond Y pays a $6\%$ semiannual coupon, has a YTM of $9\%,$ and also has $12$ years to maturity.

a$)$ What are the prices of these bonds today?

b$)$ If the interest rates remain unchanged, what do you expect the price of these bonds to be $1$ year from now? In $5$ years? In $8$ years? In $11$ years? In $12$ years?

c$)$ Plot both bonds on one graph showing Bond price versus Time to Maturity. What do you notice about the shape of the graph?