Compound Interest Calculator
See how savings or investments grow with compound interest and regular contributions, with the effect of compounding frequency and inflation made explicit.
The rule of 72, and where it stops working
Divide 72 by the interest rate and you get the doubling time. Against the exact answer, log(2) ÷ log(1 + r):
| Rate | Rule of 72 | Exact | Error |
|---|---|---|---|
| 1% | 72.00 | 69.66 | +3.4% |
| 2% | 36.00 | 35.00 | +2.8% |
| 4% | 18.00 | 17.67 | +1.9% |
| 6% | 12.00 | 11.90 | +0.9% |
| 8% | 9.00 | 9.01 | -0.1% |
| 10% | 7.20 | 7.27 | -1.0% |
| 12% | 6.00 | 6.12 | -1.9% |
| 15% | 4.80 | 4.96 | -3.2% |
| 20% | 3.60 | 3.80 | -5.3% |
| 30% | 2.40 | 2.64 | -9.2% |
| 50% | 1.44 | 1.71 | -15.8% |
It is exact at 7.85% and stays within 2% across the whole 4–12% band that ordinary saving and investing lives in. It falls apart above 20%, which is where nobody was using it anyway.
And 72 is not merely the convenient choice
The usual explanation is that 72 was picked because it divides neatly by 1, 2, 3, 4, 6, 8, 9, 12 — arithmetic you can do in your head. True, and not the whole story. Searching for the constant with the smallest worst-case error:
| Over | Best constant | Its worst error | 72's worst error |
|---|---|---|---|
| 4–12%, ordinary investing | 72 | 1.90% | 1.90% |
| 1–15% | 71.9 | 3.35% | 3.36% |
| 1–30% | 74.1 | 6.51% | 9.16% |
Over the band it is actually used in, 72 is not an approximation of the right constant — it is the right constant, to one decimal place. Only when you stretch the range past 20% does anything else win.
The constant that looks like it ought to be correct is 69.3, which is 100 × ln 2 and exact for continuously compounded interest. For interest paid once a year it is 2.9 times worse — 5.56% against 72's 1.90%. The folk rule beats the textbook one, because the folk rule is fitted to how interest is actually paid.
How to use
- Enter your starting balance and regular contribution.
- Set the rate, compounding frequency and time period.
- Read the projected balance and the interest earned.
- Compare against the inflation-adjusted figure.
Frequently asked questions
How does compound interest differ from simple interest?
Simple interest is calculated only on the original amount; compound interest is calculated on the balance including interest already earned. Over short periods the difference is small. Over decades it dominates completely, which is why the effect is described as exponential rather than merely additive.
What is the rule of 72?
A mental shortcut: dividing 72 by the annual percentage rate gives roughly the number of years for money to double. At 6 per cent, about 12 years. It is accurate enough for rates in the normal range and is the fastest way to sanity-check a projection.
Does compounding frequency matter much?
Less than people expect. Moving from annual to monthly compounding at 6 per cent raises the effective annual rate from 6 to about 6.17 per cent. Going from monthly to daily adds almost nothing further. The rate and the time period matter enormously more than the frequency.
Should I adjust for inflation?
For any projection over more than a few years, yes, or the final figure will badly mislead. A balance that looks large in nominal terms may buy considerably less than it appears. Subtracting the inflation rate from your growth rate gives a rough real return in today's money.
Why do small differences in rate matter so much?
Because the effect compounds. One percentage point of annual fees over thirty years can consume a fifth or more of the final balance, which is why fund charges receive the attention they do. The same arithmetic works in your favour for a rate improvement.
Is a fixed rate realistic for investments?
No, and that is the main limitation of any projection like this. Real returns vary year to year, and the order in which good and bad years arrive changes the outcome, particularly when you are drawing money out. A constant rate shows the shape of compounding, not a forecast, and none of this is financial advice.
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