The compounding chart

If I could keep only one table from everything I know about investing, it would be this one. It shows what a sum of money becomes at different annual returns over different periods. Nine numbers, and most of the important conclusions in long-term investing fall out of them.

The table

Annual return	10 years	20 years	30 years
7%	1.97x	3.87x	7.61x
10%	2.59x	6.73x	17.45x
15%	4.05x	16.37x	66.21x

Read it as multipliers: at 7% per year, money doubles in about a decade and turns into 7.6 times the starting sum over 30 years. The rest of this article is just reading the table slowly.

Prefer to play with the numbers? The interactive compound-interest calculator lets you pit any two annual returns against each other over any horizon — it comes pre-loaded with ingruc's real CAGR versus the S&P 500, so you can see exactly what the live edge compounds into.

Small differences become enormous ones

Look at the gap between the 7% row and the 10% row. At 10 years it is 1.97x versus 2.59x — noticeable, not life-changing. At 30 years it is 7.61x versus 17.45x. Three percentage points of annual return, held for three decades, produces well over twice the end wealth.

This is why long-term investors are obsessive about things that look petty from the outside. A fee here, a tax inefficiency there, a slightly worse average return — each shaves points off the annual rate, and the table shows what points off the annual rate cost at the far end.

The last decade does most of the work

Follow the 7% row across: 1.97x after ten years, 3.87x after twenty, 7.61x after thirty. The first decade adds about one times your starting money. The last decade adds nearly four times. Same return, same effort, wildly different payoff — because by year 20 the compounding is working on a much larger base.

The practical consequence is uncomfortable: the years that feel least productive are the early ones, and the years that matter most are the ones you only reach by not quitting. Most of the reward for patience is loaded at the end, which is precisely why patience is scarce.

Costs and taxes compound by the same mechanics

The table works in both directions. A 1.5% annual fee is not a 1.5% problem; it is a permanent downgrade of your row. An investor earning the market's 8.5% but paying 1.5% in fees lives on the 7% row instead — and over 30 years the difference between those rows, as the table shows, is not small.

Taxes on realised gains work the same way when they interrupt compounding early. This is not an argument for never paying fees or taxes; it is an argument for knowing that every recurring percentage point is being multiplied by the same machine as your returns.

What to expect, and what to doubt

Broad equity markets have historically returned somewhere around 7–10% per year nominal, over long periods, with brutal interruptions along the way. That is the realistic band. The first two rows of the table are what an ordinary, disciplined index investor can reasonably hope the decades deliver.

The 15% row exists because a small number of investors have sustained returns like it, and their results — 66x over 30 years — explain why their names are famous. But the base rate is against anyone claiming it, and anyone promising you steady 15% or more deserves your skepticism before your money. The third row is there to show what the claim implies, not to set your expectations.

Starting age matters more than starting amount

One more reading of the table. A 25-year-old investing a modest sum has a realistic shot at the 30-year column. A 45-year-old investing five times as much is working with the 10-year or 20-year column. At 7%, the 30-year multiplier is 7.61x and the 10-year multiplier is 1.97x — a gap no plausible difference in starting amounts fully closes.

The compounding machine's most important input is time, and time is the one input you cannot buy back later. The table does not tell you what to invest in. It tells you why the decision to start, made early and left alone, outweighs almost every clever decision made afterwards.