I'm having trouble calculating the convexity with Semi Annual compounding and Continuous compounding. I know how to get the Present Value of both but I don't know how to find the Weights and the Time weights.

Given: Consider a 3 year coupon bond with face value $100. Suppose Yield on the bond is 12% per annum. Coupon payments of $5 are made every 6 months.

How did we get the weights 0.040 0.037 0.035... for semi annual compounding and 0.040 0.038 0.035 0.033... for Continuous?

How did we get the Time weights 0.030 0.075 0.132... for semi annual and Time weights of 0.030 0.075 0.133... for continuous?

Example: the convexity of the previous bond is (semiannual compounding Time Cash flow Present Weight Time Weight (years value 5 47170 0.040 0.030 0.5 4.450 0.037 1.0 0.075 1.5 4.198 0.035 0.132 3.960 0.199 0.033 2.0 2.5 0.031 0.274 3.736 0.621 3.0 105 74.021 7.448 Total 130 0.798 95.08 8.157 CFt CFt (t2 t) x (1+y) P (1+y)2 (1+y)t P (1+y) (1+y)