Rule of 72 | Derivation, Uses, Extension | Quick Maths 

Remember: x here is i/100. Take small interest rate, for eg : 8% Then x is 0.08 and x squared is 0.0064 which is very small (compared to x, almost 12 times). But if interest rate is 90%, then x=0.90 and x squared is 0.81 which is not very small compared to x. Consequently, for small interest rates (less than 6%), taking 70 as the numerator would give better results, and 72 for interest rates above 10% gives better results.

Excellent thank you. So many videos on the topic, but this was the first I could find that showed a derivation