Compound Interest and the Rule of 72, Explained Simply

Compound interest is often described as the most powerful force in finance, sometimes with a quote attributed to Einstein that he almost certainly never said. The idea itself is simpler than the legend: interest that earns interest.

Simple vs compound in one example

Put 100,000 away at 8% a year for 10 years.

• Simple interest pays 8% of the original 100,000 every year: 8,000 × 10 = 80,000. You end with 180,000.
• Compound interest pays 8% of the growing balance. Year 1: 8,000. Year 2: 8% of 108,000 = 8,640. And so on. You end with about 215,892.

The extra 35,892 is interest earned on earlier interest.

The formula

A = P × (1 + r/n)^{n × t}

• A = final amount
• P = starting amount
• r = annual rate as a decimal (8% = 0.08)
• n = compounding periods per year (1 yearly, 4 quarterly, 12 monthly)
• t = years

100,000 at 8% compounded monthly for 10 years: 100,000 × (1 + 0.08/12)¹²⁰ ≈ 221,964. Monthly compounding adds about 6,000 compared with yearly, which is noticeable but much less important than the rate and the time.

Time does the heavy lifting

The second ten years add more than twice as much as the first ten. That’s the “dramatic ending” of compounding, and why starting early matters more than almost anything else.

The Rule of 72

To estimate how many years money takes to double, divide 72 by the annual percentage rate:

It works best between about 6% and 10%, and stays close enough elsewhere for quick decisions. Some people use 70 or 69 for continuous compounding; 72 is popular because it divides neatly by many numbers.

Adding money every month

Most people don’t invest one lump sum; they add a bit each month. That’s where compounding becomes really visible. Putting away 5,000 a month at 8% a year, compounded monthly:

Doubling the time more than triples the value. In the second decade the growth on your earlier savings outpaces your own monthly contributions.

It works against you too

Compounding is just as powerful on debt. A credit card balance at 24% a year doubles in about three years if nothing is repaid. That’s why paying off high-interest debt is usually a better “investment” than saving at a lower rate.

Inflation compounds as well

Prices rise in the same compounding way. Use the Rule of 72 in reverse: at 8% inflation, prices double in about nine years, so money in an account earning 4% loses buying power. What matters is the real return: interest minus inflation.

A few honest caveats

• Investments don’t earn a fixed rate every year. Compound growth calculations show a smoothed average, not a promise.
• Tax and fees reduce the effective rate, and over decades even small fees compound into large amounts.
• Some people avoid interest for religious reasons and use profit-sharing products instead; the compounding maths still describes how reinvested returns grow.

Frequently asked questions