Please take the first derivative of the bond pricing formula (P = C/(1+y) + C/(1+y)^2 + ...) with respect to "y" to get this formula

and then the second derivative to arrive at the convexity formula

Thank you

Macaulay duration =P(1+y)11C+(1+y)22C++(1+y)nnC+(1+y)nnM where P= price of the bond with semi-annual payments C= semiannual coupon interest (in dollars) y= one-half the yield to maturity or required yield n= number of semiannual periods (number of years 2, M= maturity value (in dollars) Macaulay Convexity =1nPV(CFt)1nt(t+1)PV(CFt)