Compound interest is interest calculated on an accumulated balance rather than on the original sum alone, so returns generate further returns. Over long periods the effect is not gradual but accelerating, which is why the growth curve surprises people accustomed to thinking in straight lines.

The second half of the line notes that the mechanism runs in both directions. The saver or investor holds the compounding asset and benefits from it; the borrower, particularly on credit cards or high-interest loans, is on the other side of the same arithmetic and sees the balance grow the same way.

The practical implication concerns time rather than amount. Because the effect depends on how long the compounding runs, small sums set aside early can outperform larger sums saved later, and debts left outstanding become progressively harder to clear.