Since growth rates often follow a similar pattern as the above example, economics also heavily rely on natural logarithms. Instead, it becomes somewhat stable: it's approaching a unique value already mentioned above, e ≈ 2.718281. You may notice that even though the frequency of compounding reaches an unusually high number, the value of (1 + r/m)ᵐ (which is the multiplier of your initial deposit) doesn't increase very much. Now let's check how the growing frequency affects your initial money: Now, let's imagine that your money is recalculated every minute or second: the m became a considerably high number. It is easy to see how quickly the value of m is increasing if you compare yearly (m=1), monthly (m=12), daily (m=365), or hourly (m=8,760) frequencies. Let's assume that you deposit some money for a year in a bank where compounding frequently occurs, thus m equal to a large number.
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