Why a Debt Balance Can Grow So Quickly
Interest compounds when each period’s interest is added to the balance, so later interest is charged on both the original debt and the interest already accumulated. The balance therefore grows faster than it would under simple interest, where charges are calculated only on the original amount.
The Rule of 72 is a shortcut for estimating that compounding. Behind it is an equation: a balance growing at a fixed rate reaches twice its starting size when the accumulated growth factor reaches 2. Solving that exactly involves logarithms, but for ordinary interest rates the result is close to 72 divided by the annual rate expressed as a percentage. The shortcut is convenient and works reasonably well across many common rates; it is not an exact formula.
What the Estimate Assumes
The calculation assumes the rate stays constant and interest keeps being added to the debt, with no payments or new charges changing the balance. That makes it useful for seeing the effect of a rate in isolation, not for predicting exactly when a real credit-card or loan balance will double.
In practice, payments slow or stop the growth, while fees, additional borrowing, a changing rate, or different compounding terms can alter it. A lender may also calculate interest daily or monthly, even though the shortcut uses an annual rate. For a real debt, the statement’s interest terms and payment schedule matter more than the estimate.
The rule’s memorable lesson is about time: when interest is repeatedly added to a balance, doubling can happen much sooner than intuition suggests—even without borrowing another dollar.
