Suppose the U$.$S$.$ Treasury issued $$500$ million face value of $10$ year, $7\mathrm{.}5\%$ bonds on January $15,2005$ at par value. Coupon interest is paid semi$-$annually with the face value due in $10$ years $(1/15/2015).$

a$.$ On January $14,2006,$ this bond is priced in the market to yield a stated $8\%,$ using semiannual compounding. Calculate the correct price you will pay for the bond on $1/15/2006,$ for each $$100$ of face value.

b$.$ If$,$ on the other hand, the stated yield$-$to$-$maturity of these bonds is $7\%,$ what is their price $($per $$100$ face value$)?$