Compounding, and why the early years look boring

If you have ever watched bread rise, you already understand compounding better than most textbooks explain it. Not much seems to happen for a long while. Then the last twenty minutes appear to do all the work. Money that earns a return, and then earns a return on that return, behaves exactly the same way, and the shape of it fools nearly everyone the first time. It fooled me.

The idea, in one breath

Compounding means the earnings from one period get added to the pile, so the next period's earnings are figured on a bigger pile.

The arithmetic

Here r is the return each period and n is how many periods you wait. Start with ten thousand dollars at 7 percent a year. That 7 is an example, chosen because US stocks have averaged something near it over long stretches before fees and inflation; no single year is average, and nothing promises it. After a year you have $10,700. After two, $11,449, because the second year's 7 percent was figured on $10,700 rather than $10,000. After ten years, about $19,672. After thirty, about $76,123. That last decade added more than the first two put together, and nothing about the rate changed. Only the pile did.

Two people, one lesson

Suppose Daniel saves $400 a month from 25 to 35 and then never adds another dollar. Priya starts at 35 and saves $400 a month until 65. Both earn 7 percent. Daniel put in $48,000 across ten years. Priya put in $144,000 across thirty. At 65, Daniel's $48,000 has become roughly $280,000. Priya's $144,000 has become roughly $490,000. Priya ends with more, and she should, but look at what Daniel did: a third of the money, more than half the result, because his early dollars had twenty extra years to work. Every one of these assumptions is yours to change in the calculator, and I would encourage you to change them until the lesson feels like your own.

What the neat illustrations leave out

Real returns do not arrive at a steady 7 percent. They come lumpy, with whole years of loss, and the order they arrive in matters a great deal to someone who is drawing money out. Fees are subtracted before the compounding happens, so a 1 percent fee on a 7 percent return is really compounding at 6, which over thirty years costs about a quarter of the ending balance. Inflation quietly shrinks what that ending number will buy. And taxes take their share depending on which account the money sat in, which is why the account guides live next door to this one.

Questions worth asking yourself

What return are you assuming, and where did that number come from? What gets subtracted before the compounding, in fees and in taxes? How would a bad decade at the start, or at the end, change the picture? And the one I would sit with longest: if the plan only works at 10 percent, what happens at 5?