Bond $x$ is a premium bond making semiannual payments. The bond has a coupon rate of $12$ percent, a YTM of $10$ percent, and $12$

years to maturity. Bond $Y$ is a discount bond making semiannual payments. This bond has a coupon rate of $10$ percent, a YTM of $12$

percent, and also has $12$ 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 $3$ years? In $7$ years? In

$11$ years? In $12$ years?

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

Answer is not complete.