Bond X is a premium bond making semiannual payments. The bond has a coupon rate of $9$ percent, a YTM of $7$ percent, and $13$ years to maturity. Bond Y is a discount bond making semiannual payments. This bond has a coupon rate of $7$ percent, a YTM of $9$ percent, and also has $13$ years to maturity. Both 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 $1$ year from now? In $4$ years? In $8$ years? In $12$ years? In $13$ years?