Stop using e for compound interest

Summary

Stop using e for compound interest In a typical math class, e is introduced like this:Imagine a bank account with 100% yearly interest. This means that anything you deposit will be doubled a year later.The bank decides to compound interest twice yearly, instead of once per year. Then, every 6 months, your deposit will increase by 50%, letting you leave with 2.25x the amount you put in.The bank now decides to compound interest daily, meaning that your deposit will increase by 100365% 365 times. After a year, you can leave with approximately 2.714x.Finally, the bank compounds interest continuously, letting you leave with exactly e times the amount you put in after a year.This makes sense mathematically, and in class, e=limn→∞(1+1n)n.But here's the problem: why is compound interest divided linearly even though the growth is exponential? If a bank account has 100% yearly interest that compounds twice yearly, it would make more sense to grow by 2−1 every 6 months instead of 50%. This would keep the total yearly return consistent.Because of this, banks have to publish the interest rate, compound interval, and annual percentage yield separately.e doesn't need to be introduced this way. It has many other nice properties:exp⁡z is the only function that is its own derivative (a fixed point for the derivative operator) with the condition of exp⁡0=1.eix=cos⁡x+isin⁡x, so eiπ=−1, and eiτ=1.In general, ex is periodic with a period of iτ, showing a delightful connection between exp and trigonometric functions.None of these topics (calculus, complex analysis, and trigonometry) require prior knowledge about e specifically, so why bring it up using compound interest?