Compound Interest and the Rule of 72, Explained Simply
Why starting to save ten years earlier can double your result, how the rule of 72 works, and what compounding frequency really changes.
Compound interest is often called the most powerful force in personal finance. The idea is simple: you earn returns not only on the money you put in, but on the returns you have already earned. Over short periods the effect is modest. Over decades it does most of the work.
Simple vs compound interest
Suppose you invest $10,000 at 7% a year.
- With simple interest you earn $700 every year. After 30 years you have $10,000 + 30 × $700 = $31,000.
- With compound interest each year's $700-and-growing is added to the balance and earns 7% too. After 30 years you have $10,000 × 1.07³⁰ = $76,123.
The difference, about $45,000, is interest earned on interest.
The rule of 72
To estimate how many years it takes money to double, divide 72 by the annual percentage rate.
| Annual return | Years to double (rule of 72) | Exact |
|---|---|---|
| 3% | 24 | 23.4 |
| 6% | 12 | 11.9 |
| 8% | 9 | 9.0 |
| 10% | 7.2 | 7.3 |
| 12% | 6 | 6.1 |
The rule works in reverse for debt and inflation. A credit card at 24% doubles an unpaid balance in about three years. Inflation of 3% halves the purchasing power of cash in about 24 years.
Time matters more than amount
Consider two savers who each earn 7% a year:
- Alex invests $300 a month from age 25 to 35, then stops. Total contributed: $36,000.
- Sam invests $300 a month from age 35 to 65. Total contributed: $108,000.
At 65, Alex has about $420,000 and Sam about $366,000. Alex contributed one-third as much but ended with more, purely because the money had ten extra years to compound. You can reproduce this with the compound interest calculator.
Does compounding frequency matter?
Banks advertise daily or monthly compounding, but the effect is smaller than many people expect. At a 5% nominal rate:
- Annual compounding gives an effective rate of 5.000%.
- Monthly compounding gives 5.116%.
- Daily compounding gives 5.127%.
On $10,000 over a year, daily versus annual compounding is worth about $13. The rate itself and the length of time matter far more. When comparing savings accounts, look at the APY (annual percentage yield), which already includes compounding.
What eats into compounding
- Fees. A 1% annual fund fee on a 7% return leaves 6%. Over 30 years that shrinks the final balance by about a quarter.
- Taxes. Tax-advantaged accounts such as 401(k)s, IRAs and ISAs let returns compound without being taxed each year.
- Withdrawals. Taking money out early removes not just that money but all its future growth.
- Inflation. A 7% nominal return with 3% inflation is about a 4% real return.
Putting it to work
Start as early as you can, even with small amounts. Automate contributions so they happen without effort. Keep costs low by choosing low-fee index funds. And leave the money alone so it can compound. Use the savings goal calculator to find the monthly amount needed for a specific target, or the retirement calculator to see where your current habits lead.