Miller Corporation has a premium bond making semiannual payments. The bond has a coupon rate of $12$ percent, a YTM of $10$ percent, and $18$ years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond has a coupon rate of $10$ percent, a YTM of $12$ percent, and also has $18$ years to maturity. Both bonds have a par value of $$1,000.$

a$.$ What is the price of each bond today? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ If interest rates remain unchanged, what do you expect the price of these bonds to be $1$ year from now? In $9$ years? In $13$ years? In $17$ years? In $18$ years? $($Do not round intermediate calculations and round your answers to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[,,,$liller Bond,Modigliani Bond$],[$a$.,$Price today,$$,1,146\mathrm{.}99ox,850\mathrm{.}61$