Compound Interest: The Formula, a Worked Example, and Its Limits
Compound interest means that previously earned returns are added to the amount that earns future returns. With a constant annual rate, an illustrative future value is principal × (1 + rate)^years. Real investments have changing returns, fees, taxes, and risk, so the formula models an assumption rather than a promise.
Calculate a transparent example
If 1,000 units earn a fixed 5% once each year and all returns stay invested, the model gives 1,000 × 1.05² = 1,102.50 after two years. Simple interest on the original 1,000 would produce 1,100 under the same simplified assumptions. The difference starts small and grows as the number of periods rises. The units here are illustrative; this is not an offer, forecast, or personal investment recommendation.
What the rule of 72 can and cannot tell you
Dividing 72 by an annual percentage rate gives a rough estimate of years to double: at 6%, about 12 years. It is a shortcut, not a replacement for the full calculation, and it becomes less accurate when the rate changes or contributions and withdrawals occur. Inflation also changes what a doubled nominal amount can buy.
A useful way to read the book
Before applying a worked example, list its assumptions: starting amount, rate, compounding interval, fees, and time. Change one assumption at a time and compare the result. Dr. Alaa Theeb’s Arabic book “سحر الفائدة المركبة” also uses compounding as an analogy for repeated habits. That analogy can motivate reflection, but human behavior does not follow a guaranteed financial equation.
Common questions
How does compound interest differ from simple interest?
Simple interest is calculated on the original principal. Compound interest includes accumulated returns in the amount used for later calculations.
Does the formula guarantee an investment result?
No. It produces a result for the rate and timing you enter. Actual returns, costs, and purchasing power may differ substantially.
View the Arabic book about compounding
The linked book and reader are in Arabic. This English guide is editorial context, not a translation of the book or a promise of a particular result.