Number $ e $ formula significance

Question

Number $ e $ was formed using Compound interest formula $ ( 1 + \frac 1 n ) ^ n $. when $ n $ becomes so large $ e $ will approach constant $ 2.7182818 $. In the same way if we alter formula to be $ ( 1 + \frac 2 n ) ^ n $ then also it approach a irrational constant $ 7.389041 $. This is true with any number. So, what was significance about using $ 1 $ and naming it as $ e $.

Answer 1

Just notice that: $$\lim_{n\to\infty} (1+\frac{a}{n})^n = e^a$$