In yesterday’s post about the benefits of compound interest (especially if you happen to be frozen in cryonics lab for 1000 years), there’s a note that Fry would have earned an additional $1.2 billion if the interest on his account had been compounded continuously instead of annually. It’s not unusual to find places that compound quarterly, monthly, or even daily, but are there really institutions that compound continuously? The answer, surprisingly, is yes.
Or at least, there used to be. In the article “A Tale of Two Banks,” Craig Miller explains how in the 1970s compounding wasn’t done as frequently as today, both because of the market and because of technological limits. At one point, though, two banks began to use the frequency of compounding as a way to compete with each other: one advertised weekly, the next daily, and then the first announced that it would compound continuously. The second bank followed, and Miller was hired to write the appropriate code. (The article itself contains many more details of the scenario, and is certainly worth a read!)
I haven’t seen any modern institutions that compound more often than daily, even in the fine-print of our credit card statements, but it does me good to know that the continuous compounding examples I’ve used when teaching exponential functions do have a real-life historical counterpart.