Exponential constant ‘e’
The exponential constant is denoted by e. Its value is approximated at 2.718 and called as Euler number or Napier’s constant.
Swiss mathematician Jacob Bernoulli discovered the Euler number while researching compound interest.
In recognition of John Napier, a Scottish mathematician who pioneered the use of logarithms, this value is referred to as the Napier constant.
The letter e was used by Euler for exponents, consequently, the letter is now commonly connected with his name.
Euler’s number (e) is an important part of math. It is what exponential functions and logarithms are based on.
Understanding ‘e’ in Bernoulli’s way
Assume lending money with an interest rate of 100% that added up every year. Your money would be worth twice as much in a year.
What if the rate of interest was cut in half and added twice as often?
Your money would grow 225 percent in a year at 50% every six months.
which is (1+100%/2)2
As the interval shrinks, total returns rise.
Jacob Bernoulli observed that if interest is calculated n times each year at a rate of 100%/n, the total accumulated wealth after the conclusion of the first year will be little more than 2.7 times the initial investment.
| n | (1 + 100%/n)n or (1+1/n)n |
| 1 | 2.00000 |
| 2 | 2.25000 |
| 5 | 2.48832 |
| 10 | 2.59374 |
| 100 | 2.70481 |
| 1,000 | 2.71692 |
| 10,000 | 2.71815 |
| 100,000 | 2.71827 |
It is approaching e. i.e., 2.718 and is how Jacob Bernoulli first discovered it.
Therefore, ‘e’ is an irrational number, its decimal expansion never ends.
General Formula :
Euler introduced e in math computations. Compound interest is calculated using the formula: Pert
