Bond $x$ is a premium bond making semiannual payments. The bond has a coupon rate of $8$ percent, a YTM of $6$ percent, and $20$ years to maturity. Bond $Y$ is a discount bond making semiannual payments. This bond has a coupon rate of $6$ percent, a YTM of $8$ percent, and also has $20$ years to maturity. Both bonds have a par value of $$1,000.$

a$.$ What is the price of each bond today?

b$.$ If interest rates remain unchanged, what do you expect the price of these bonds to be $1$ year from now? In $11$ years? In $15$ years? In $19$ years? In $20$ years?

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

$\backslash$table$[[,$Bond $x,$Bond $Y$