A $20$ year $4\%$ coupon bond is currently selling at a price of $$103\mathrm{.}50.$ This bond has a face value of $$100.$ Find the duration and convexity of this bond using the approximate formulas $($use $10$ basis point change in yield$).$ Calculate the price of the bond if the yield goes up by $20$ basis points using the duration and convexity. SHOW ALL STEPS, DO NOT USE EXCEL