Logan Corp. issued a non$-$ callable bond that has $16$ years to maturity, an $7\%$ semi$-$annual coupon, and a $$1\mathrm{.}000$ par value. Your required return on the Logan Corp. Bond is $9\%$; if you buy it$,$ you plan to hold it for $12$ years. You $($and the market$)$ have expectations that in $12$ years, the yield to maturity on a $4-$year bond with similar risk will be $6\%.$

A$)$ how much should you be willing to pay for the Logan Corp. Bond today?

B$)$ Does the Logan Corp. Bond face greater or less price risk than a bond with $16$ years to maturity and a $3\%$ semi$-$annual coupon?