Compound Growth Explained: The Snowball and the Rule of 72

Compound growth is what happens when your money's earnings start earning money of their own. In year one a $10,000 investment at 8% earns $800. Leave that $800 invested and year two earns $864 — $64 of it paid on the first year's gain. That second layer feels trivial, but given decades it becomes the majority of everything you own. Compounding is the entire reason ordinary savers retire with seven figures.

The mechanics: growth on growth

The formula is A = P x (1 + r)^t — final amount equals principal times one-plus-the-rate raised to the number of years. The exponent is the whole story: returns multiply rather than add, so time has an outsized effect. Ten years at 8% multiplies money by 2.16, but thirty years multiplies it by 10.06 — three times the years, nearly five times the growth.

Year 1: $10,000 + $800 = $10,800
Year 2: $10,800 + $864 = $11,664
Year 3: $11,664 + $933 = $12,597
Year 10: $21,589 — the money has doubled once
Year 20: $46,610 — doubled twice more
Year 30: $100,627 — and the curve is now climbing almost vertically

The rule of 72: doubling time in your head

Divide 72 by your annual return and you get the years needed for money to double. At 8%, money doubles every 9 years; at 6%, every 12; at 12%, every 6. It is an approximation — exact within a few percent for returns between 4% and 15% — and it makes compounding tangible: a 30-year-old's dollar at 8% doubles roughly four times before age 66, turning $1 into about $16.

Why starting early beats investing more

The table below shows three savers, identical in everything except start date, each contributing $500 a month until 65 at an 8% average return. The early starter does not win by a little — the early starter laps the field.

Starting at 25 instead of 35 adds $60,000 of contributions but roughly $1,000,000 of ending wealth — each extra early dollar did the work of seventeen. To catch up from a 35-year-old start, you would need to contribute about $1,170 a month, not $500. Time is the one input no raise, bonus or windfall can buy back later, which is why how to start investing puts starting above optimizing.

Compounding's four enemies

• Fees — a 1% annual fee does not cost 1% of your money; it drops your compounding rate from 8% to 7% and consumes about a quarter of a 30-year ending balance. Details in fees and expense ratios explained.
• Taxes — annual taxes on gains skim the snowball each year, which is why tax-advantaged accounts compound visibly faster than taxable ones at the same return.
• Inflation — an 8% nominal return with 3% inflation is a 4.85% real return; always check what your money actually earns after prices rise, as covered in inflation and real returns.
• Interruption — selling in a panic resets the exponent. The gains compound in proportion to time unbroken, which is why the worst compounding decision is the temporary exit.