See the snowball effect of compounding on your money
| Year | Starting Balance | Contributions | Interest | Ending Balance | Total Interest |
|---|
Compound interest is interest earned on interest. Unlike simple interest (which only pays on your original principal), compound interest grows exponentially because each period's interest is added to the principal, and the next period's interest is calculated on the new, larger balance.
This is why Albert Einstein reportedly called compound interest "the eighth wonder of the world." Given enough time, even modest returns can produce extraordinary results.
A = P × (1 + r/n)n×t
| Compounding | $10,000 at 7% for 20 years | Extra vs. Annual |
|---|---|---|
| Annual (n=1) | $38,697 | — |
| Quarterly (n=4) | $40,178 | +$1,481 |
| Monthly (n=12) | $40,483 | +$1,786 |
| Daily (n=365) | $40,540 | +$1,843 |
The more frequently interest compounds, the more you earn — but the difference between monthly and daily compounding is usually small (less than 0.2% per year).
Invests $5,000/year from age 25–35 (10 years, $50k total), then stops.
At 7%, her $50k grows to $562,000 by age 65.
Invests $5,000/year from age 35–65 (30 years, $150k total).
At 7%, his $150k grows to $505,000 by age 65.
The lesson: Emma invested $100,000 less but ended up with $57,000 more, all because she started 10 years earlier. Time matters more than the amount you invest.
The Rule of 72 lets you estimate how long it takes to double your money: divide 72 by your annual return rate. At 7%, your money doubles every ~10.3 years (72 ÷ 7 = 10.29). At 10%, it doubles every ~7.2 years.
| Year | Simple Interest (7%) | Compound Interest (7%) | Difference |
|---|---|---|---|
| 5 | $13,500 | $14,026 | +$526 |
| 10 | $17,000 | $19,672 | +$2,672 |
| 20 | $24,000 | $38,697 | +$14,697 |
| 30 | $31,000 | $76,123 | +$45,123 |
Starting with $10,000 at 7% annual rate. The gap widens dramatically over time — this is the snowball effect in action.