$1.$ A bond with a $$10,000$ par value has an $4\%$ coupon rate. It will mature in $5$ years, and coupon payments are made annually. Using a discount rate of $3\mathrm{.}95\%,$ value this bond?

A$.9,872\mathrm{.}15$

B$.9,981\mathrm{.}35$

C$.10,022\mathrm{.}49$

D$.10,133\mathrm{.}74$

$3.$ If the bond in the previous question is trading at $$9,500,$ then what required return are investors demanding? Which one is right $?$

A$.5\mathrm{.}16\%$

B$.5\mathrm{.}00\%$

C$.5\mathrm{.}38\%$

$4.$ You are holding a $7$ year, $10\%$ semiannual coupon bond. The bond$$s current price is $$900.$ What is the bond$$s current ytm$?$ Assuming $50$ basis point changes, what is the bond$$s approximate duration and approximate convexity?? Find both the approximate duration and convexity assuming $50$ bp change.