Rule of 72 Calculator
Calculate how long it takes to double your money using the Rule of 72 with our free calculator. This powerful mental math shortcut helps investors quickly estimate investment growth—simply divide 72 by your expected annual return to find the doubling time.
Rule of 72 Quick Reference
| Annual Return | Years to Double | Example |
|---|---|---|
| 2% | 36 years | Savings account |
| 4% | 18 years | Conservative bonds |
| 6% | 12 years | Balanced portfolio |
| 8% | 9 years | Growth stocks |
| 10% | 7.2 years | S&P 500 historical |
| 12% | 6 years | Aggressive growth |
| 15% | 4.8 years | Exceptional performance |
How the Rule of 72 Works
Years to Double = 72 ÷ Annual Interest Rate
For example:
- At 6% return: 72 ÷ 6 = 12 years to double
- At 8% return: 72 ÷ 8 = 9 years to double
- At 10% return: 72 ÷ 10 = 7.2 years to double
Rule of 72 Calculator
``javascript
function ruleOf72(annualRate) {
const yearsToDouble = 72 / annualRate;
const actualYears = Math.log(2) / Math.log(1 + annualRate/100);
// Calculate growth over multiple doublings
const doublings = [1, 2, 3, 4, 5];
const growthTable = doublings.map(d => ({
doublings: d,
years: (yearsToDouble * d).toFixed(1),
multiplier: Math.pow(2, d) + 'x'
}));
return {
yearsToDouble: yearsToDouble.toFixed(1),
actualYears: actualYears.toFixed(2),
accuracy: ((yearsToDouble / actualYears) * 100 - 100).toFixed(1) + '% error',
growthProjection: growthTable
};
}
`
Using Rule of 72 for Other Calculations
The rule works in reverse too: to find the rate needed to double in N years, divide 72 by N. Want to double your money in 10 years? You need 72 ÷ 10 = 7.2% annual returns. The rule also applies to inflation—at 3% inflation, prices double every 24 years.
The Projection Behind This Page
Starting from $10,000, adding $200 a month at 7%:
| Year | Deposited | Balance | Growth | Growth on deposits |
|---|---|---|---|---|
| 1 | $12,400 | $13,201 | $801 | 6% |
| 5 | $22,000 | $28,495 | $6,495 | 30% |
| 10 | $34,000 | $54,714 | $20,714 | 61% |
| 20 | $58,000 | $144,573 | $86,573 | 149% |
After 20 years, 60% of the balance is growth rather than money you
put in. That crossover — the point where returns exceed contributions — is the whole reason
compounding is worth waiting for, and it arrives later than most people expect.The Formula
`
A = P(1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) ÷ (r/n)]
└── initial principal ──┘ └────── regular contributions ──────┘
`
The second term usually dominates. On these numbers the $200 monthly contribution
accounts for the larger share of the final balance, which is the practical lesson: how much
you add matters more than the rate, right up until the balance gets large.
How Long Until It Doubles
The Rule of 72 divides 72 by the rate to estimate doubling time. At 7%:
`
72 ÷ 7 = 10.3 years
`
The exact answer is 10.2 years — the rule is accurate to within a few months
for rates between 6% and 10%, and drifts at the extremes. It works because ln(2) ≈ 0.693 and
72 has convenient divisors.
| Rate | Rule of 72 | Exact |
|---|---|---|
| 2% | 36.0 yr | 35.0 yr |
| 5% | 14.4 yr | 14.2 yr |
| 7% | 10.3 yr | 10.2 yr |
| 10% | 7.2 yr | 7.3 yr |
| 15% | 4.8 yr | 5.0 yr |
Compounding Frequency at This Rate
A nominal 7% turns into a different effective yield depending on how often it
compounds — this page uses annually:
| Compounded | Effective annual yield |
|---|---|
| Annually | 7.000% |
| Quarterly | 7.186% |
| Monthly | 7.229% |
| Daily | 7.250% |
| Continuously | 7.251% |
The gap between annual and monthly is worth having. The gap between monthly and daily is
0.021 percentage points — rounding. Compare accounts on
APY, which already folds the frequency in, rather than on the nominal rate.Inflation Is the Number That Matters
A 7% nominal return against 3% inflation is a 4.0% real return.
Real return is what buys anything:
`
real ≈ nominal − inflation
``
Over 10 years, 3% inflation cuts purchasing power by about 26%. A projection quoted in nominal dollars therefore overstates what the money will actually be worth, which is why retirement targets are usually stated in today's dollars.