Compound Interest Explained, with the Rule of 72
Compound interest is the reason a modest amount saved early can outgrow a larger amount saved later. It is also the reason high-interest debt grows so quickly. Once you see the arithmetic, the most useful habit in personal finance becomes obvious: start early and let time do the work.
Key takeaways
- Compounding means earning returns on your past returns, not only on what you put in.
- $10,000 growing at 7% a year becomes about $76,100 after 30 years without adding a cent.
- Investing $300 a month for 40 years at 7% grows to about $787,000; doubling the amount but starting 10 years later reaches only about $732,000.
- The Rule of 72: divide 72 by the annual rate to estimate how many years it takes to double.
Simple vs compound growth
With simple interest, $10,000 at 7% earns $700 every year: after 30 years you would have $31,000. With compound interest, each year’s $700-plus is added to the balance and earns returns itself. After 30 years you would have about $76,123, more than double the simple-interest result from the same rate.
Future value = P × (1 + r ÷ n)^(n × t)
P is the starting amount, r the annual rate, n the number of compounding periods per year and t the number of years. Regular contributions add a second term, which is what most calculators handle for you.
Why starting early beats saving more
Compare two savers who both earn 7% a year, compounded monthly:
| Saver | Monthly amount | Years invested | Total contributed | Balance at the end |
|---|---|---|---|---|
| Starts at 25 | $300 | 40 | $144,000 | about $787,400 |
| Starts at 35 | $300 | 30 | $108,000 | about $366,000 |
| Starts at 35, saves double | $600 | 30 | $216,000 | about $732,000 |
The ten-year head start more than doubles the final balance. Even saving twice as much from age 35 does not catch up with the early starter, despite contributing $72,000 more. The last decade of compounding does the heavy lifting, and you only get it if you start early.
Enter a starting amount, a monthly contribution and a rate, then compare starting now with starting five years later.
The Rule of 72
To estimate how long money takes to double, divide 72 by the annual rate:
Years to double ≈ 72 ÷ annual rate (%)
- At 7%: 72 ÷ 7 ≈ 10.3 years (exact: 10.24 years).
- At 6%: 72 ÷ 6 = 12 years (exact: 11.9 years).
- At 3% inflation: prices double in about 24 years, so today’s $1,000 buys only about half as much by then.
- At 24% on a credit card: an unpaid balance doubles in about 3 years.
The rule works in reverse too. To double your money in 8 years you need about 72 ÷ 8 = 9% a year.
Small differences in rate, big differences in outcome
Over long periods, a single percentage point matters enormously. $300 a month for 30 years grows to about $366,000 at 7% but only about $301,000 at 6%. That $65,000 gap is what a 1% annual fee can cost. When comparing funds or pensions, the ongoing charge deserves as much attention as past performance.
The things that work against compounding
Inflation
A 7% return with 3% inflation is roughly a 4% gain in purchasing power. For long-term goals, think in today’s money by using a return figure after inflation, or adjust the target with an inflation calculator.
Taxes
Taxes on interest and gains each year slow compounding. Tax-advantaged accounts such as a 401(k), IRA, UK ISA or pension let growth compound without that annual drag. See 401(k) vs IRA vs Roth IRA.
Interruptions
Withdrawing early, or pausing contributions for years, resets the clock on the money removed. Keeping an emergency fund separately protects long-term investments from short-term needs.
Debt compounds too
Compounding works against you on debt. Paying off a card at 23% is like earning a guaranteed 23% return, which no investment reliably offers.
A note on realistic returns
The 7% used in these examples is illustrative, not a forecast. Investment returns vary from year to year and can be negative. Test a lower rate as well as your base case, and treat any projection as a range rather than a promise.
Frequently asked questions
What is the difference between simple and compound interest?
Simple interest is paid only on the original amount. Compound interest is paid on the original amount plus the interest already earned, so growth accelerates over time.
How accurate is the Rule of 72?
It is very close for rates between about 6% and 10%. At 7%, it predicts doubling in 10.3 years; the exact answer is 10.24 years. At very high or very low rates the error grows.
Does compounding frequency matter much?
A little. Monthly compounding beats annual compounding at the same stated rate, but the difference is small compared with the effect of the rate itself, fees and time.
What return should I assume for long-term investing?
Use a conservative figure and test more than one, for example 5% and 7% a year, and lower for portfolios with more bonds or cash. Past returns do not guarantee future ones.
Sources
This guide is general information to help you understand the numbers. It is not financial, tax or legal advice. Rates, limits and rules change, so check official sources or a qualified adviser before making a decision. Read our full disclaimer.