Compound Interest

What is compound interest?

Compound interest is interest earned not only on your original money but also on the interest it has already earned. With simple interest you earn the same amount every period, because it is always calculated on the starting principal. With compounding, each period's interest is added to the balance, so the next period earns interest on a slightly larger sum — and that snowballs. Over short spans the difference is small, but because the balance grows by a percentage of itself each period it grows exponentially, and over long horizons the gap becomes dramatic. Three levers drive the outcome: the interest rate, the length of time you leave it invested, and how often interest is compounded (yearly, monthly, daily). Time is the most powerful of these — the same rate over twice the years does far more than double the growth, which is why starting early matters so much. A handy shortcut, the rule of 72, estimates the doubling time by dividing 72 by the percentage rate.

How the simulation shows it

You set a principal, an interest rate, and a number of years, and watch the balance curve away from what simple interest would give — the compounding gap widening as the horizon grows. Changing the rate or the years yourself makes exponential growth intuitive rather than a formula: doubling the time more than doubles the result.

Common misconceptions

• Compound growth isn't a straight line. Because each period earns interest on the previous interest, the balance curves upward — small early differences become large ones over time.
• Time matters more than you'd think. Doubling the number of years far more than doubles the final balance, so starting early beats contributing more later.
• A higher rate isn't the only lever. Compounding frequency and, above all, the length of the horizon can matter as much as the interest rate itself.

Frequently asked questions

What is the difference between simple and compound interest?

Simple interest is always calculated on the original principal, so you earn the same amount each period. Compound interest is calculated on the growing balance, so you earn interest on your interest and the total grows faster.

Why is compound growth exponential?

Because each period's balance grows by a percentage of itself, and that percentage applies to an ever-larger sum. Growth feeds on itself, producing a curve that steepens over time rather than a straight line.

Why does starting early matter so much?

Because time is compounding's most powerful lever: the same rate left for twice as long produces far more than twice the growth, so money invested earlier has more periods to snowball.

What is the rule of 72?

A shortcut for estimating how long money takes to double: divide 72 by the annual percentage rate. At 6%, for example, a balance doubles in roughly 12 years.

Does compounding frequency change the result?

Yes. Compounding more often — monthly or daily instead of yearly — adds interest to the balance sooner, so it earns a little more, though the effect is smaller than that of the rate and the time horizon.