How Compound Interest Works — and What It Cannot Promise

With compound interest, returns are added to the balance and then earn returns of their own. Over a few years the effect is small; over decades it dominates. The same arithmetic runs in reverse on debt. But it only multiplies the rate you actually get, which nobody can guarantee; inflation takes part of it, and fees more than most people expect.

What is happening

Figures are in neutral units; the rates are scenarios, not forecasts. One deposit of 10,000 units, with returns added once a year (value = 10,000 × (1 + rate)^years):

With 6% simple interest (returns paid out, not reinvested) the same deposit reaches only 16,000, 22,000 and 28,000. The interest on interest is 1,908 units after 10 years, 10,071 after 20 and 29,435 after 30: most of the gap appears late.

Regular saving: 100 units at the end of every month, returns added monthly:

The rule of 72 is a shortcut: 72 divided by the annual rate in percent gives the approximate number of years to double. At 6% it says 12 years against an exact 11.9, at 8% it is almost exact, at 2% it is a year out (36 against 35), and at 20% it says 3.6 against 3.8.

It works against you too. A debt at 24% a year that you do not pay down doubles in about three years (3.2 with interest added yearly). That is why paying only the minimum on a card can keep a balance alive for years, and why the real cost of a loan depends so much on its length.

Nominal is not real. The real return is (1 + nominal) ÷ (1 + inflation) − 1, not a simple subtraction: 6% with 3% inflation is 2.9% real, so the 57,435 units after 30 years buy about what 23,662 bought at the start. A return equal to inflation leaves you where you began: at 4% with 4% inflation, 32,434 units after 30 years buy what 10,000 did.

Fees compound too. A fee taken every year as a percentage of the balance removes a share of the final amount equal to 1 − (1 − fee)^years, whatever the return:

So 1% a year takes about a quarter of the final sum over 30 years and about a third over 40. The US Securities and Exchange Commission gives a similar example: $100,000 growing at 4% for 20 years ends at about $208,000 with a 0.25% annual fee and about $179,000 with a 1% fee (SEC).

Early or big? A common claim: a small amount invested at 25 beats three times as much at 40. It depends on the return. One deposit at 25 against a triple deposit at 40, both left until 65: the early one ends ahead only if the return is above about 7.6% a year. Yearly contributions from 25 against triple yearly contributions from 40: the threshold is about 6.6%. Those are nominal rates; at a real 3–5% the later, larger saver finishes ahead. Starting early buys time, but it does not replace the size of what you put in.

What to do

• Know your total yearly cost in percent: fund, platform and advice fees. See check fees before returns and index funds.
• Compare any return with inflation over the same period before calling it growth (raises below inflation).
• Start with what you have (start investing with what you have) and raise contributions when you can: the amount matters as much as the start date (start saving for retirement early).
• Treat a guaranteed high return, or returns that are unusually smooth, as a warning sign: the SEC (US) lists both as red flags of Ponzi schemes. See investing versus speculating.
• Pay off expensive debt first: its compounding usually outruns what investments earn (high-interest debt first).

When this is not the case

• Money you need soon. Over a few years a risky investment can be worth less than you put in; markets do not grow at a steady rate. See never invest money you need soon.
• No rate is guaranteed. Every rate on this page is a scenario, and the past returns of any market are not a forecast.
• Taxes on investment income reduce the result as well; the rules and tax-advantaged accounts depend on the country.

Sources

• SEC (US) — How fees and expenses affect your investment portfolio
• SEC (US) — Ponzi schemes
• Calculations: the formulas are given in the text; all rates are scenarios.

Checked: 24 September 2026