A bond portfolio named VEX, comprises four bonds $($face value$=$$$1000)$:

$1)100$ semi$-$annual bond, $5-$year maturity, a coupon rate of $4\%$

$2)200$ annual bonds, $30-$year maturity, $8\%$ coupon bond.

$3)300$ zero coupon bonds, $10-$year maturity.

$4)400$ zero coupon bonds, $20-$year maturity.

$4)$According to the duration$-$price formula with Macaulay$$s duration D$,$ if the yield increases from $6\%$ to $8\%,$ the VEX$$s market value should fall by how much $($$$)?(10\%$ credit$)$

$5)$Calculate each bond$$s convexity using Excel template. Then calculate VEX$$s portfolio convexity $($detailed calculation of each bond$$s convexity must be presented$).$

Bond $1($semi$-$annual coupon bond$)$:

$17\mathrm{.}58$

Bond $2($annual coupon bond$)$:

$212\mathrm{.}43$

Bond $3($zero coupon bond$)$:

$99\mathrm{.}77$

Bond $4($zero coupon bond$)$:

$380\mathrm{.}95$

Considering VEX$$s convexity, when the yield increases from $6\%$ to $8\%,$ the VEX$$s market value should fall by how much $($$$)?(10\%$ credit$)$

$6)$What is the difference of price drop between a formula with and without convexity? $(10\%$ credit$)$

$7)$Repeat question $4,5,$ and $6$ if the yield decreases from $6\%$ to $4\%.(20\%$ credit$)$

Please only use and show formulas in excel