Bond $x$ is a premium bond making semiannual payments. The bond has a coupon rate of $10$ percent, a

YTM of $8$ percent, and $16$ years to maturity. Bond $Y$ is a discount bond making semiannual payments. This

bond has a coupon rate of $8$ percent, a YTM of $10$ percent, and also has $16$ 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 $7$ years? In $11$ years? In $15$ years? In $16$ years?

Note: For all requirements, do not round intermediate calculations and round your answers to $2$

decimal places, e$.$g$.,32\mathrm{.}16.$