$1)$If you have a bond with face value $$100$ coupon rate $9\%$ and YTM $6\%$ semiannual and $20$ years to maturity $.$ If YTM changes by $20$ bp calculate the approximated convexity.

$2)$ If you have a bond with yield$-$to$-$maturity $8\%.$ The approximate modified duration is $9$ and approximate convexity is $105.$ What is the estimated Delta in price resulting from a $100$ bps decrease in the yield$-$to$-$maturity? How much of that adjustment is due to convexity?

$3)$ If you have a bond with $$1000$ face value pays annual coupon rate $6\%$ with YTM $6\%$ and $3$ years to maturity calculate the Macaulay duration. If YTM for the same bond changes to $10\%$ what is the new Macaulay duration and what is your takeaway from this change?

$4)$ If the modified duration is $6\mathrm{.}8$ and YTM dropped by $75$bp$,$ and bond is selling at its face value of $$1000$ what is the projected new price?