How compound growth works

Why the first ten years feel broken

Almost everyone who starts investing has the same private thought around year three. This is not working. The balance looks like the deposits and very little else, and the promised snowball is nowhere.

Nothing is wrong. That is what the early part of the curve looks like. Compounding is back loaded by construction, and the years that feel pointless are the ones buying the years that are not.

The mechanism, in one paragraph

Put in $1,000 and earn 7 percent. You now hold $1,070. The next 7 percent is calculated on $1,070 rather than $1,000, so it pays $74.90 instead of $70. That extra $4.90 is the whole idea. It is small once. It is not small four hundred times.

Growth joins the base and then earns alongside it. Every layer you add starts earning too, which is why the curve bends upward instead of climbing in a straight line.

The formula that actually applies

Two different formulas get used interchangeably here, and only one fits most people's situation.

For a single deposit left alone, future value is A = P(1 + r/n)^nt. That covers a lump sum. Most people are not investing a lump sum. They are adding money every month, which is the future value of an annuity:

FV = PMT × [((1 + i)^N − 1) ÷ i]
where i is the monthly rate (the rate that, applied twelve months in a row, compounds to exactly the annual rate) and N is the number of deposits.

The distinction matters more than it looks. Run the lump sum formula on a contribution stream and you will overstate the result badly, because it assumes every dollar was present from day one.

Thirty years of $300 a month

Assume $300 every month at a 7 percent annual return, compounded monthly. Nothing else. No raises, no windfalls, no clever timing.

After ten years you have handed over $36,000 and hold about $51,316. Growth contributed roughly $15,316. Respectable. Not the stuff of magazine covers.

Hold the identical habit for thirty years and the picture stops being modest. You have contributed $108,000. The balance is about $350,836, of which roughly $242,836 is growth. You tripled the time and the result multiplied by nearly seven.

Read those two paragraphs again and notice what did not change. Not the monthly amount, not the return, not the strategy. Only the number of years.

What the long record actually shows

Seven percent is an assumption, so it is fair to ask where a number like that comes from.

Over 1928 to 2025, the S&P 500 returned roughly 10 percent a year in nominal terms, against inflation of about 3 percent, according to the historical series maintained by Aswath Damodaran at NYU Stern. Across a longer window and a wider net, Dimson, Marsh and Staunton put world equities at 5.2 percent a year after inflation over the 125 years from 1900 to 2024.

Those are averages across a century of wars, panics and recoveries. No individual decade is obliged to cooperate.

Two things that spoil the arithmetic

The first is variance. Markets do not deliver the average, they wander around it. The S&P 500 has finished up in roughly three years out of four since 1928, which also means it finished down in the fourth. A projection is a center line through a wide cone of outcomes, not a payment schedule.

The second is inflation, which compounds in the wrong direction. At roughly 3 percent a year, purchasing power halves about every twenty four years. A balance thirty years out will not buy what the same figure buys today, so every projection on this site carries an inflation adjusted twin and the calculators plot both.

None of this makes compounding less real. It makes the honest version of it slower and less certain than the version in the advertisement, which is the version worth planning around.