As the title says, how come the value e is special? it has functions and rules just dedicated to it, but what sets it apart from another random number?
In: 397
I’ll try to do it without equations.
Imagine you have money in a high risk savings account. Let’s say $1000, which is earning 100% interest per year. If interest is calculated once, at the end of the year, you would have $2000, right?
Suppose I now say the annual rate is still 100% but I’ll calculate the interest and add it on to your original amount every six months. (So 50% return each half year).
This would make you $250 better off! (As you now *also* get the second half of the year’s 50% on the first half of the year’s $500 interest.)
So, the more often we calculate the interest, the better – even though the yearly return is still 100%
Let’s take it further. If the interest calculation was monthly, then the yearly return would be $1613. So 2.61 times your starting amount by me just splitting your 100% return into smaller slices.
So the question is – how far can we take this? What effective return would we get if we recalculated daily? hourly? every minute?
Well it turns out that the answer is ‘e’. If we could recalculate the 100% interest every second or less then we would get end up with $2718.28
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