doubling rule

a fairly reasonable rule for calculating how long an investment amount would take to double
given a fixed compound percentage increase is:

rate R(%) times the time (in years) to double is roughly 69

so the time to double an invested amount is roughly 69/R

sometimes the rule is quoted using 72 rather than 69 (with more factors probably...)
[ln(2) = 0.693... is where the 69 comes from]

an adjustment suggested to give a better estimate is time to double (t) = (69.3/R) + 0.34

students working on compound interest, using a multiplier and a calculator, could explore the amount of time taken to double an initial amount (like £1000)

wiki has more detail on the matter, including some history