MathsFrancais2 min de lectureMis a jour 2 avr. 2026

Simple vs. Compound Interest: The Magic of Growth

Unlock the secret to wealth building. Learn why Albert Einstein called compound interest the "eighth wonder of the world" and how math transforms small savings into large fortunes.

Points Cles

Simple Interest is calculated only on the original principal amount.
Compound Interest calculates interest on both the principal AND previous interest.
Compounding frequency (Daily vs. Annually) significantly impacts long-term returns.
The "Rule of 72" is a mental shortcut to estimate when an investment will double.
Inflation creates "Negative Compounding," eroding the purchasing power of idle cash.

Two Paths to Financial Growth

Mathematics offers two ways to earn money on your money. Simple interest is linear—it grows predictably and slowly. Compound interest is exponential—it starts slow but accelerates massively over time. Understanding this distinction is the difference between surviving and thriving financially.

Simple Interest: The Linear Model

Simple interest is straightforward. You earn a fixed percentage of your original deposit every year. Because the "base" never changes, your earnings never increase. ``` Formula: I = P x r x t ``` (Interest = Principal x rate x time). If you put $1,000 into a simple interest account at 10%, you earn $100 every year. In 10 years, you have $2,000.

Compound Interest: The Exponential Model

With compound interest, the interest you earn today is added to your balance tomorrow. Next year, you earn interest on that *new, higher* amount. You are essentially earning "interest on interest." ``` Formula: A = P(1 + r/n)^(nt) ```

Growth Comparison: $10,000 over 30 Years

See how a 7% return behaves differently under both systems over a long-term horizon. ``` | Year | Simple Interest (7%) | Compound Interest (7%) | Gap (The Yield) | | --- | --- | --- | --- | | 0 | $10,000 | $10,000 | $0 | | 10 | $17,000 | $19,671 | +$2,671 | | 20 | $24,000 | $38,696 | +$14,696 | | 30 | $31,000 | $76,122 | +$45,122 | ```

The Rule of 72: A Mental Masterclass

Want to know how long it takes to double your money without a calculator? Use the **Rule of 72**. Divide 72 by your interest rate, and the result is the number of years required. - **At 6%**: Doubling takes 12 years (72 / 6). - **At 10%**: Doubling takes 7.2 years (72 / 10). - **At 2%**: Doubling takes 36 years (72 / 2).

Step-by-Step: The First Year of Compounding

Let's track $1,000 at 10% compounded monthly: ``` 1. Principal: $1,000. 2. Monthly Rate: 10% / 12 = 0.833%. 3. Month 1 Interest: $1,000 x 0.00833 = $8.33. New Balance = $1,008.33. 4. Month 2 Interest: $1,008.33 x 0.00833 = $8.40. New Balance = $1,016.73. ``` Result: After just two months, you are already earning more interest than you did in the first month because your balance grew.