Compounding and inflation

Time is a force

Two forces work on every amount of money over time. One makes it grow: returns that earn returns of their own. The other quietly shrinks it: rising prices.

Neither is visible from one day to the next. Over ten, twenty or thirty years, both become enormous. Understanding them explains why the time horizon matters so much, why small differences in return or cost add up, and why cash under the mattress is not as safe as it looks.

Growth on growth

With simple interest, you earn the same amount every year on your original money. With compound interest, or compounding, each year's return is added to the amount, so next year you earn on the bigger number. The SEC's investor website shows it with 100 at 5%: 105 after one year, and 110.25 after two, because the second year's interest is also paid on the first year's interest.

In the first years the two lines are almost identical. Over decades they separate dramatically. With a fictional 1,000 growing at 5% a year, simple interest gives 2,500 after 30 years, and compounding gives about 4,322. Real investments never grow this smoothly, of course. The chart assumes exactly the same rate every year to show the mechanics.

Notice where most of the growth happens: at the end. Of the roughly 3,322 gained with compounding, about half arrives in the last ten of the thirty years, when the growing amount earns on itself the most. That is why time does so much of the work.

A handy shortcut is the rule of 72: divide 72 by the yearly rate to estimate how many years it takes for money to double. At 6%, about 12 years. At 9%, about 8. It is a rule of thumb, not an exact calculation.

Compounding works in both directions. Fees and losses compound too. A fee of 1% a year sounds small, but over decades it takes a large share of the final amount, because every year it also removes the future growth on the money it took.

The other force

Inflation is the general rise in prices over time. When prices rise, the same amount of money buys less: your purchasing power falls. Many central banks aim for low and stable inflation. The European Central Bank targets 2% over the medium term, and the US Federal Reserve aims for 2% over the longer run.

Take the fictional 1,000 from above again, growing at 5% a year for 30 years, while prices rise 2% a year:

• In money, it grows to about 4,322.
• In today's purchasing power, that is worth about 2,386, because prices have risen by about 81% over the same 30 years.

That is why returns are often judged as a real return: the return after inflation. Roughly, 5% growth with 2% inflation is about 3% in real terms. And money that earns nothing loses purchasing power every year that inflation is above zero.

Common mistakes

• "A few percent don't matter." Over decades, small differences in return or fees grow into large differences in the result.
• Expecting smooth compounding. Real investments go up and down. The smooth curves assume the same rate every single year.
• Ignoring inflation. A 2% interest rate with 3% inflation means losing purchasing power.
• Trying to replace time with risk. Starting late and taking big risks to catch up usually adds risk, not time.
• Comparing returns over different periods. 20% over five years is not the same as 20% a year.
• "Cash is always safe." Its nominal value stays the same, but with inflation above zero, what it can buy shrinks every year.