Even with more frequent compounding, there is a limit you cannot cross
Suppose you invest 1,000,000 won at an annual interest rate of 100%. With annual compounding it becomes 2,000,000 won. What happens if interest is compounded every six months, every month, every day, or every second? Surprisingly, no matter how often it is compounded, it never exceeds about 2,718,281 won.
Formula: If one year is divided into n compounding periods, the final amount is principal × (1+1/n)ⁿ. As n grows without bound, this value converges to the special constant e ≈ 2.71828.... Increase n below and observe the convergence.
Value of (1 + 1/n)ⁿ
2.00000
1,000,000 won → 2,000,000 won
💡 e is a famous mathematical constant, like π. It appears as the base of the natural logarithm, in calculus, probability and statistics, and even in the mathematics of spiral shell shapes.