Compounding

The Eighth Wonder Is Just Arithmetic

Compounding gets quoted like scripture. It is slower and simpler than that, and the math is small enough to check yourself.

August 2026 · 4 min read

"Compound interest is the eighth wonder of the world." You have seen the line. It usually has Einstein's name under it.

He almost certainly never said it. Nobody has ever found it in anything he wrote or was recorded saying, and versions of it were floating around in advertisements before his name got attached. A good line travels further with a genius stapled to it.

So skip the quote and do the arithmetic. The arithmetic is the interesting part, and it is small enough to check on your phone.

Twenty dollars a week

Take $20 a week. Put it somewhere paying 4% a year. Add nothing else. Never miss a week.

After 5 years you have $5,754. You deposited $5,200.
After 10 years you have $12,781. You deposited $10,400.
After 20 years you have $31,846. You deposited $20,800.

Those are weekly deposits at a 4% annual rate compounding weekly. The 4% is a round number chosen to make the math legible. It is not a rate MORE quotes and it is not a forecast. On-chain stablecoin yields float, and they have often been lower than that.

Look at what the numbers actually say. At year 10, four out of every five dollars in that account are dollars you put there. Compounding did something, but you did most of it.

At year 20 the interest is $11,046, which is more than half of everything you deposited. Run it to 30 years and you have $60,283 against $31,200 of deposits. The yield has almost caught up to you. That late bend is the part people mean when they say the word compounding.

The curve is back loaded, and that is the whole problem

Year one of that plan earns about $21 of interest. Twenty one dollars, for fifty two weeks of showing up.

Year twenty of the same plan, with the same $20 a week, earns about $1,227.

Nothing changed except the size of the pile doing the earning. This is why compounding feels fake for the first few years and obvious in hindsight. The boring early years pay almost nothing, and they are the only reason the later years pay anything at all.

A quick sanity check you can do in your head: divide 72 by the rate to approximate the doubling time. At 4% that is 18 years. Run it exactly and 1.04 to the 18th power is 2.03. Close enough to be useful.

The deposit is the bigger lever, for a long time

Traders instinctively optimize the rate. Early on, the rate is the smaller lever by a wide margin.

Ten years of $20 a week at 4% gets you $12,781. The same $20 a week at 0% gets you $10,400. A decade of yield bought you $2,381. Doubling the deposit to $40 a week, at zero yield, would have gotten you $20,800.

That is not an argument against yield. It is an argument about where to spend your attention. The rate is a slider you adjust once. The deposit is a decision you have to make several hundred times, which is exactly why most plans die there.

Where a trader's deposit comes from

If you are trading, you are already producing the input. Not profit. Volume.

$10,000 of monthly volume at 1% is $100 a month.
$25,000 of monthly volume at 1% is $250 a month.
$100,000 of monthly volume at 1% is $1,000 a month.

Run the middle one out. $250 a month at 4% for ten years is $36,812. Of that, $30,000 is the skim and $6,812 is yield.

The honest caveats: volume is not steady, vault rates float, and a bucket holding Bitcoin moves with Bitcoin instead of paying a coupon. These are illustrations of arithmetic, not projections of your account.

The wonder is boring

The eighth wonder is not a rate. It is the same small action surviving a thousand weeks in a row.

Compounding plans almost never fail on the math. They fail in week nine, when the market is interesting and $20 feels irrelevant, and then again in week forty when you have stopped thinking about it entirely. Every missed deposit is also missing all the interest that deposit would have earned for the next twenty years.