I share the formula here. Though you will need a calculator and get your hands dirtier for a more accurate answer.
https://toc.net/2019/10/14/compounding-interest-and-rule-of-72/
your post is good.
i just want to add a few points
carry a table everywhere is troublesome. i carry my hp. it comes with a simple calculator. my compound interest formula is (1.0x)^n where x is the interest and n is the number of years.
your understanding of the rule of 72 is good. but it did not reflect how the 72 is developed.
if you look at the denominator, ln(1+r). you can do a maclaurin expansion of the term. it becomes r - 0.5r^2 + 0.17r^3.
the maclaurin expansion can be used because r is usually a small number.
r is a decimal number. eg 0.02 for 2%. to convert it to a whole number, you multiply your formula by 100 on the numerator and denominator.
100*ln2 = 69.3. this is not a very convenient number. it cannot be divided by many numbers. a slight bigger number has to be chosen becoz of the -0.5r^2. 72 is the pick because it can be divided by many numbers.
the limitation of maclaurin is that the r must be a small number. so if you are into a ponzi scheme, then the formula breaks down.
this is my personal analysis of the 72 rule. you can tear it down if you have enuf maths to do it