What Is Compound Interest

Imagine you put 100 dollars in a savings account. The bank pays 10 per cent interest each year. After one year, you have 110 dollars.

In the second year, the bank pays interest on the whole 110 dollars, not just your first 100. So you earn 11 dollars, and you have 121. In the third year, you earn interest on 121. This is compound interest: you earn interest on your money and also on the interest you already earned.

At first, the extra money is small. But over many years, it grows faster and faster. This is why people say: start saving young. Time is more powerful than the amount.

Compound interest also works the other way. If you owe money on a credit card and do not pay it back, the debt grows in the same way — interest on interest. This is why credit card debt can become a big problem very quickly.

Simple interest is paid only on the original sum. Compound interest is paid on the original sum plus all the interest that has already accumulated — interest earning interest. That small difference changes the shape of the growth from a straight line into a curve that steepens over time.

A rough guide is the "rule of 72": divide 72 by the annual percentage rate and you get the approximate number of years for the money to double. At 6 per cent, a sum doubles in about 12 years; at 8 per cent, in about 9. Because doubling then happens again, and again, the results over a working lifetime can look implausible from the starting point.

The key variable is time, not the amount invested. Someone who saves modestly from age 25 typically ends up ahead of someone who saves much more but starts at 40, simply because the early contributions have more doubling periods ahead of them.

The same mathematics runs in reverse on debt. Unpaid credit-card balances, where rates are often 20 per cent or more, compound rapidly, and a manageable debt can grow faster than a person can repay it. Understanding compounding is less about clever investing and more about a basic orientation: start early, be patient, and treat high-interest debt as urgent.

Compound interest is arithmetic, but its consequences are so counter-intuitive that they function almost as a cognitive illusion. Human intuition extrapolates linearly; compounding is exponential, and over long horizons the two diverge to a degree that the starting figures give no hint of.

The mechanism is simply that each period's interest is added to the base on which the next period's interest is calculated. The rule of 72 offers a usable shortcut: dividing 72 by the annual rate approximates the doubling time, and because doublings recur, a sum left untouched for several decades at a modest real rate can multiply many times over. The dominant input is not the contribution but the number of compounding periods, which is why the marginal value of a unit of money saved falls sharply with the age at which it is saved.

The symmetry with debt is exact and, for most households, more consequential. Revolving credit at rates in the twenties compounds against the borrower on the same curve, and once the interest accrual outpaces repayment capacity the balance can enter a self-reinforcing climb. Much of what is marketed as sophisticated personal finance reduces, in practice, to positioning yourself on the favourable side of this curve and off the unfavourable side.

There is a distributional dimension worth naming. Compounding rewards capital that can be left to work undisturbed, which correlates with already having a financial buffer; it penalises those forced to borrow at high rates to smooth volatile income. A mechanism that is neutral as mathematics is, embedded in an unequal society, a quiet amplifier of that inequality over time.