My only favorite math equations
My two favorite math equations are:
1.01365 = 37.8, and
0.99365 = 0.03.
These equations explain the power of small (one percent) daily changes over the course of a full year (365 days).
If we make something one percent better every day for a year, we make it 37 times better. And if we make something one percent worse every day for a year, we make it 97% worse.
Small changes make a huge difference over a long period of time. We often apply this concept to our finances (e.g. compounding interest). But we can also apply it to our organizations, relationships, and personal abilities.
Each day, you’re either getting better or getting worse. You don’t have to make huge changes today to see massive progress over the next year. You only have to focus on getting a little bit better every day.
Explaining the math
Using me as an example, let’s assume I can make myself a little bit better at basketball every day for a full year, starting today.
I’ll start out as one whole me. So, we’ll represent me with the number 1. Each day, I will make a small improvement. Let’s represent the improvement as 0.01 or 1%. In other words, I’m going to make myself 1% better every day.
We’re focused on days. So, let’s represent the year as the number 365. If I make myself (1) one percent better (0.01) every day for a year (365), I will make myself 37 times, or 3700%, better by the end of the year. Here’s how the math works.
On the first day, I will make myself 1% better. This equates to 1 multiplied by 0.01, which equals 0.01. At the end of the day, we add the improvement (0.01) to me (1). Now I’m 1.01.
On the second day, I will again make myself 1% better. Since I’m now 1.01, this equates to 1.01 multiplied by 0.01, which equals 0.0101. At the end of the day, we add the improvement (0.0101) to me (1.01). Now I’m 1.0201.
After 363 more days of this, I’ll be approximately 37 times better at basketball, rounding down. In math, this is equal to 1.01 (or 1 + 0.01) multiplied by itself 365 times.
We express this as 1.01 to the 365th power, or 1.01365.