Bond X is a premium bond making semiannual payments. The bond has a coupon rate of $7\mathrm{.}5$ percent, a YTM of $6$ percent, and $13$ years to maturity. Bond Y is a discount bond making semiannual payments. This bond has a coupon rate of $6$ percent, a YTM of $7\mathrm{.}5$ percent, and also $13$ years to maturity. Assume the interest rates remain unchanged and a $$1,000$ par value.

a$.$

What are the prices of these bonds today? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What do you expect the prices of these bonds to be in one year? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ What do you expect the prices of these bonds to be in three years? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

d$.$ What do you expect the prices of these bonds to be in eight years? $($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 bonds to be in $12$ years? $($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 $13$ years? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$