Question

Arnulfo deposited $55 into a savings account for which interest is compounded semiannually. According to the rule of 72, what interest rate will cause his money to double in approximately 23 years?

Answer 1

The "rule of 72 formula"
rate needed to double your money = 72 / years
rate = 72 / 23 = 3.13%

I could adjust the "rule of 72 formula" so that it calculates a semi-annual rate, but it would make the calculation a LOT more difficult than just dividing 72 by the rate.

Rather than that, let's calculate the EXACT rate to double money in 23 years.
http://1728.org/compint.htm
For annual compounding it is 3.05955 %
For semi-annual compounding it is 3.0365 %