I vaguely recall that method. I was curious as to why it works and am somewhat embarrassed to say that I couldn’t figure it out right away. I did a Web search and found this simple explanation. It all boils down to the facts that you can use natural logarithms to solve problems involving continuous interest and that ln(2) = .693, which is close to .70. You get from decimal representation of an interest rate to percent by multiplying by 100 and if you also multiply .693 by 100, you get 69.3, which is close to 70. Follow the link for the details.
Continuous interest is not the same as interest compounded yearly, which is what I originally computed. For most calculations the difference is relatively minor. Using the formula in the link to compute what the continuous interest rate would be, we get
650,000 = 53,000 e**(40r).
650/53 = e**(40r).
Taking the natural log of both sides gives 40r = ln(650/53). Performing the calculation on the right and dividing by 40 gives about 6.3%.