How long does it take for your money or debt to double? Explaining the rule of 72 to students

Abstract

The ‘rule of 72’ provides a useful approximation of when an investment or debt will double. Students can apply it for an estimate, avoiding mistakes later when using technology for a precise answer. On standardized tests, moreover, such devices may be disallowed. In job interviews, too, quickly approximating the doubling answer demonstrates the impressive problem-solving ability. Illustrations abound online and in traditional media showing how to use it. This is not the same as explaining why it works or the limitations. Inquiring students want to know. This paper combines familiar territories in math and application to provide a relatively simple mathematical explanation.