There are four bonds $($A$,$ B$,$ C and D$)$ with diffefrent charateristics as follws.

Bond Price Coupon rate Time$-$to$-$maturity Yield$-$to$-$maturity

A $5\%5$ years $7\%$

B $8\%5$ years $7\%$

C $5\%10$ years $7\%$

D $8\%10$ years $7\%$

Answer the following questions in the specific order $($the numbers in the parentheses are the points for each of the quesitons$)$:

$(1)$ Calculate the price $($value$)$ for each of the bonds, assuming the coupons are paid annually. $(4)$

$(2)$ Which bonds are premium bonds? Which bonds are discount bonds? $(1)$

$(3)$ Are you able to figure out which would be premium, and which would be discount, bonds without any calculation? Explain why or why not. $(2)$

$(4)$ Compare Bonds A and C: which bond's price will change more if the market interest rate changes? $(1)$ Why? $(1)$

$($Hint: You do not need to do any calculation to answer question $(5))$