Bond $x$ is a premium bond making semiannual payments. The bond pays a coupon rate of $7\mathrm{.}1$ percent, has a YTM of $6\mathrm{.}4$ percent, and

has $13$ years to maturity. Bond $Y$ is a discount bond making semiannual payments. This bond pays a coupon rate of $6\mathrm{.}4$ percent, has a

YTM of $7\mathrm{.}1$ percent, and also has $13$ years to maturity. The bonds have a par value of $$1,000.$

What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year

from now? In three years? In eight years? In $12$ years? In $13$ years?

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