$($Question$1)$ A bond with a $$1,000$ face value, $8$ years to maturity with a $7\%$ coupon is currently selling for $$967\mathrm{.}32.$ If market interest rates fell by $3\%,$ what would happen to the price of this bond and why?$($Question $2)$ Suppose we are interested in a seven$-$year $7\mathrm{.}5\%$ coupon bond with annual payments. A broker quotes a price of $$937\mathrm{.}14$ What is the yield on this bond?$($Question $3)$ A bond has a yield to maturity of $7\mathrm{.}3\%$ and coupon payments of $$80$ annually. What do we know about the price of this bond relative to its face value $($assume it is $$1\mathrm{.}000.)($Question $4)$ What would be the yield to maturity for a $20-$year bond that pays a $$40$ coupon semi$-$annually $($$$40$ twice a year$)$ with a face value of $$1\mathrm{.}000.$ that is currently selling for $$987\mathrm{.}94?($Question $5)$ You currently have two different bonds in your portfolio: Bond A has $9$ years left till maturity, and it pays an $8\%$ annual coupon. Bond B has $4$ years left and is paying a $10\%$ coupon. If market interest rates increase by $3\%,$ which bond's price will be more greatly impacted?