Bond $x$ is a premium bond making semiannual payments. The bond has a coupon rate of $8\mathrm{.}7$ percent, a YTM of $6\mathrm{.}7$ percent, and has $20$ years to maturity. Bond $Y$ is a discount bond making semiannual payments. This bond has a coupon rate of $6\mathrm{.}7$ percent, a YTM of $8\mathrm{.}7$ percent, and also has $20$ years to maturity. Assume the interest rates remain unchanged and both bonds have a par value of $$1,000.$

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

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ What do you expect the prices of these bonds to be in one year?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

c$.$ What do you expect the prices of these bonds to be in three years?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

d$.$ What do you expect the prices of these bonds to be in eight years?

Note: Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

e$.$ What do you expect the prices of these $ onds to be in $12$ years?

Note: Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

f$.$ What do you expect the prices of these bonds to be in $20$ years?

Note: Do not round intermediate calculations.