What "compound" actually means
Simple interest is calculated only on your original amount (the principal), every period, forever. Compound interest is different: after each period, the interest you earned gets added to your balance, and the next period's interest is calculated on that new, larger balance — including the interest you just earned. In other words, you start earning interest on your interest, not just on your original contribution. This "interest on interest" effect is small at first but accelerates over time, which is why compound growth looks close to a straight line for the first few years and then curves sharply upward over longer horizons.
The Rule of 72: a quick mental shortcut
The Rule of 72 is a simple approximation for how many years it takes an amount to double at a given constant annual compound rate: years to double ≈ 72 ÷ annual rate (as a whole number, not a decimal). It's not perfectly exact — it's a well-known approximation of the true logarithmic doubling-time formula — but it's accurate enough for quick mental comparisons across different rates.
Rule of 72 examples
| Annual rate | Years to double (72 ÷ rate) |
|---|---|
| 6% | 12.0 years |
| 7% | 10.3 years |
| 10% | 7.2 years |
This is a useful gut-check tool: at a 7% return, your money roughly doubles every decade. Over a 30-year working career, that's not just one doubling — it's closer to three, which is part of why starting to save earlier has such an outsized effect on your final balance compared to saving the same total amount later.
Worked example: compound vs. simple interest over 30 years
To make the difference concrete, here's $10,000 invested for 30 years at a 7% annual rate, compared under both simple and compound interest — no additional contributions, just the original $10,000 left to grow:
$10,000 at 7% for 30 years
| Simple interest | Compound interest (annual) | |
|---|---|---|
| Interest earned | $21,000.00 | $66,122.55 |
| Final balance | $31,000.00 | $76,122.55 |
Simple interest: $10,000 + ($10,000 × 7% × 30 years). Compound interest: $10,000 × (1.07)30, compounded once per year. This site's retirement calculator compounds monthly rather than annually, which produces a slightly higher final balance for the same nominal annual rate — try the same $10,000 starting balance, $0 monthly contribution, 7% return, 30 years there to see the monthly-compounding version.
Compound interest more than doubles the total growth compared to simple interest on the exact same principal, rate, and time period — over $45,000 more in this example — purely because of interest earning interest on itself. This gap widens the longer the money stays invested, which is the mathematical basis for the common retirement-savings advice to start contributing as early as possible.
Why this matters for retirement savings specifically
Regular retirement accounts (401(k)s, IRAs, taxable brokerage accounts) benefit from this same compounding mechanic, but with monthly or more frequent contributions added on top of the growth — which is what this site's retirement calculator models. Two people who each end up contributing the same total dollar amount over their careers can end up with very different final balances if one started contributing 10 years earlier than the other, purely because of how many compounding periods their early contributions had to grow.
Frequently asked questions
Is the Rule of 72 exactly accurate?
No, it's a well-known approximation. The exact doubling time formula involves natural logarithms (ln(2) / ln(1 + rate)), but the Rule of 72 gets close enough for mental math across the rate ranges (roughly 4%-15%) most commonly discussed in personal finance.
Does compounding frequency (monthly vs. annually) matter a lot?
It matters, but less dramatically than the rate itself or the time horizon. More frequent compounding (monthly vs. annually) at the same nominal annual rate produces a modestly higher effective return, because interest starts earning its own interest sooner. This site's retirement calculator compounds monthly for a more realistic approximation of how most investment and savings accounts actually work.
Is a 7% return guaranteed?
No. 7% is commonly cited as a long-run historical average for a diversified stock-heavy portfolio before inflation, but no investment guarantees a fixed return, and actual year-to-year results vary significantly. See the retirement calculator's notes on this for more detail, and the guide on how much to save for retirement for broader planning benchmarks.
Does compound interest apply to debt too?
Yes — the same mechanic works against you with compounding debt (like credit card balances), which is part of why unpaid high-interest debt grows so quickly. See debt avalanche vs. snowball for strategies on paying down debt efficiently.