A $$2,0007\%$ three$-$year bond has semiannual coupons and redemption amount

$$2,225.$ It is purchased to provide the investor with a $5\%$ annual effective yield.

Find the Macaulay convexities $C(4\%,),C(5\%,),$ and $C(6\%,).$ Also

compute the modified convexity $C(5\%,2).$