Compound interest, explained with real numbers

Compound interest is interest that earns interest. That six-word definition is easy to nod along to and easy to underfeel — because its consequences over decades are genuinely unintuitive, and the people who internalise them early end up with startling advantages over the people who don't. This page walks the arithmetic slowly, with numbers you can check against the compound interest calculator as you go.

Simple versus compound

Put $1,000 at 8% simple interest and you earn $80 a year, every year: after 30 years, $1,000 + 30 × $80 = $3,400. The interest never joins the principal, so year thirty pays the same as year one.

At 8% compound, each year's interest is added to the balance before the next year's is calculated: $1,000 → $1,080 → $1,166.40 → … after 30 years, about $10,063. Same rate, same deposit, three times the money — and the entire difference is the interest earning its own interest.

The mechanics, slowly

Watch the first few years to see the snowball form. Year one earns $80. Year two earns 8% of $1,080 — $86.40, of which $6.40 is interest on interest. Year three: $93.31. The increments look trivial, which is exactly why people underrate them; but each year's growth is proportional to a balance the previous years fattened. By year 20 the annual interest is about $345; by year 30 it's about $745 — nine times the original $80, from the same deposit at the same rate. Exponential growth spends its early years looking boring. That's not a flaw in the deal; it is the deal.

The Rule of 72

The doubling time of compounding money is approximately 72 divided by the interest rate. At 8%, money doubles about every 9 years; at 6%, every 12; at 3%, every 24. It's a back-of-envelope approximation (excellent between about 4% and 12%), and it turns vague rates into vivid facts: 8% for 36 years is four doublings — ×16. It also prices delay: at 8%, a ten-year wait costs you one entire doubling — the last one, the biggest.

Why starting early beats saving more

The classic comparison, worth running honestly. Saver A puts in $200/month from age 25 to 35, then never deposits again. Saver B puts in $200/month from 35 all the way to 65. At 8% annual growth, compounded monthly:

• A deposits $24,000 and reaches roughly $400,000 at 65 — the balance from the ten early years compounds untouched for thirty more.
• B deposits $72,000 — three times as much — and reaches roughly $300,000.

A third the money in, a bigger pile out, purely because A's dollars each got more doublings. The lesson isn't "stop contributing at 35" — A contributing throughout would have both piles. It's that time in the market is the input compounding rewards most, and the years you don't start are the expensive ones. Run your own ages and amounts in the calculator; the shape survives any reasonable numbers.

Does compounding frequency matter?

Less than people hope. $10,000 at 6% for 10 years: annual compounding gives $17,908, monthly $18,194, daily $18,220. Monthly-versus-annual is worth having; daily- versus-monthly is a rounding error. The variables that actually move the outcome are rate, time and contributions — in roughly that order of glamour and the reverse order of controllability. You control time most, contributions next, rate barely. Spend your attention accordingly.

The same force, pointed at you

Every mechanism above runs identically in reverse on borrowed money. A credit-card balance at 24% APR has a Rule-of-72 doubling time of three years — unpaid, $3,000 becomes $6,000, then $12,000. Minimum payments are calibrated to barely outrun the compounding, which is why balances feel immortal: on a typical card, minimums take decades to clear. The practical order of operations follows directly: high-interest debt is a guaranteed 24% "return" when paid off, which no investment reliably beats — kill it first, then point the snowball the profitable direction and give it as many years as you have.