Compound Interest: The Eighth Wonder of the World
Albert Einstein reportedly called compound interest the eighth wonder of the world. Whether or not he actually said it, the math is undeniable: money grows exponentially when interest earns interest.
Simple vs Compound Interest
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest on | Principal only | Principal + accumulated interest |
| Growth | Linear | Exponential |
| Formula | A = P(1 + rt) | A = P(1 + r/n)^(nt) |
The Compound Interest Formula
// A = Final amount
// P = Principal (initial investment)
// r = Annual interest rate (decimal)
// n = Compounds per year
// t = Years
A = P * (1 + r/n) ^ (n * t)
// Example: $10,000 at 8% for 30 years, monthly compounding
A = 10000 * (1 + 0.08/12) ^ (12 * 30)
A = $109,357.30The Impact of Time
Starting early matters more than investing more later:
| Scenario | Monthly | Years | Total Invested | Final Value (8%) |
|---|---|---|---|---|
| Start at 25 | $200 | 35 | $84,000 | $414,000 |
| Start at 35 | $400 | 25 | $120,000 | $296,000 |
| Start at 45 | $800 | 15 | $144,000 | $175,000 |
The person who started at 25 invested the least but ended up with the most. That's the power of time and compounding.
With Regular Contributions
// Future value with monthly contributions
// PMT = monthly contribution
FV = P * (1 + r/n)^(n*t) + PMT * (((1 + r/n)^(n*t) - 1) / (r/n))Real vs Nominal Returns
Don't forget inflation. If your investment returns 10% but inflation is 4%, your real return is approximately 6%. Always think in real terms when planning long-term savings.
See how your money can grow over time with the PureTools Savings Simulator. Enter your initial amount, monthly contribution, interest rate, and time horizon to visualize your wealth growth curve.