Miller Corporation has a premium bond making semiannual payments. The bond pays an $10$ percent coupon, has a YTM of $8$ percent, and has $20$ years to maturity. The Modigliani Company has a discount bond making semiannual payments. This bond pays a $8$ percent coupon, has a YTM of $10$ percent, and also has $20$ years to maturity. $($Do not round intermediate calculations. Round the final answers to $2$ decimal places. Omit $ sign in your response.$)$

If interest rates remain unchanged, what do you expect the price of these bonds to be $1$ year from now? $10$ years? $15$ years? $19$ years? $20$ years?