Compound interest

Simple vs compound

Simple interest pays only on the original sum. Compound interest pays on the original sum plus all the interest already added. So the base you earn on keeps growing — interest earning interest earning interest. Over a year or two the gap is small. Over decades it is enormous, because the growth is exponential, not linear.

The formula

A = P (1 + r/n) ^ (n t)

P = starting amount      r = annual rate (e.g. 0.08)
n = compounds per year   t = years      A = final amount

The exponent is the point. Time, t, sits up in the power — so adding years does far more than adding money.

A worked example

Invest $10,000 at 8% a year, compounded annually. After 10 years it is about $21,600. After 20 years, about $46,600. After 30 years, about $100,600. The money roughly doubled in the first decade — and then each later decade added far more than the one before, with no extra deposits. That acceleration is compounding.

The Rule of 72

A quick mental shortcut: divide 72 by the annual rate to get the years it takes to double. At 8%, money doubles roughly every 72 / 8 = 9 years. At 6%, every 12 years. It tells you instantly why a couple of extra percentage points, left alone for long enough, change everything.

It runs in reverse too

The same force powers debt. Credit-card balances compound against you — often monthly, at 20%+ — so unpaid interest joins the balance and starts charging its own interest. The lesson cuts both ways: start saving early and leave it alone, and never let high-interest debt sit and compound. Time is the lever — it works for whoever is on the right side of it.