How compound interest actually works

Compound interest is interest earning interest: each period's growth is added to the balance, and the next period's growth is calculated on the new, larger total. The definition fits in a sentence. The consequences take decades to play out, and the early ones are so small that many people quietly conclude the whole thing is oversold — which is precisely how they lose the years the mechanism needed most.

The shape to hold in mind is slow-then-sudden. Compounding spends its first decade looking like a rounding error and its third doing things that look like typos, and every practical decision it touches — when to start, how much the rate matters, what a debt balance does when ignored — follows from that shape.

Growth on growth

Start with the contrast that isolates the mechanism. Simple interest pays on the original principal only: $10,000 at 6% earns $600 a year, every year, and after thirty years you hold $28,000. Compound interest pays on the whole balance, growth included, so the first year's $600 is the smallest amount of growth the account will ever produce.

The gap column is the mechanism made visible. After ten years it reads as a curiosity; after thirty it is $29,435 — more than the simple account's entire thirty years of interest. Slice the compound column by decade and the acceleration is plainer still: the same untouched $10,000 grows by $7,908 in its first decade, $14,163 in its second, and $25,364 in its third. The last decade out-earns the first two combined. Nothing improved along the way — no deposits were added, no better fund was found. The only thing that changed is that the balance doing the earning had grown.

Where the account lives changes the tax, not the arithmetic. Inside a TFSA the compounding runs untouched; in a taxable account, each year's tax bill skims off growth that would itself have compounded, which behaves exactly like a permanently lower rate — and the price of a slightly lower rate, as the fee example below shows, is much larger than it sounds.

Why time beats rate

Two savers, identical in every respect but one: the start date. Each puts $300 a month into the same portfolio returning 7% a year, compounded monthly. One starts now; the other starts ten years from now.

Starts nowStarts in year 10

Same deposit, ten years apart

	Starts now	Starts in year 10
Year 0	0	0
Year 10	51925	0
Year 20	156278	51925
Year 30	365991	156278

$300 per month at a 7% annual return, compounded monthly. The late starter's curve is the early starter's curve shifted ten years to the right — the distance between them grows every year.

After thirty years the early starter holds about $366,000 on $108,000 of deposits. The late starter, twenty years in, holds about $156,000 on $72,000. The gap is not the $36,000 of missed deposits — it is roughly $210,000, because the missing years were the ones at the point on the curve where each year is worth the most.

There is no catching up, either; that is what the chart is quietly showing. The late curve is the early curve shifted ten years right, so the distance widens rather than closes — the crossover people imagine never comes. Doubling the effort does not force one: at $600 a month the late starter deposits $144,000 in total, more than the early starter ever will, and still finishes near $313,000 — behind someone who saved half as much per month. Actually matching the early starter's final balance from ten years back takes about $703 a month. Ten missing years cost more than double the monthly effort, sustained for twenty years.

The multiplier tells the same story from another angle: the early starter's deposits grew to 3.4 times what went in, the late starter's to 2.2 times. Same behaviour, same fund, same rate — the difference was bought entirely with time.

The same arithmetic prices interruptions. Cashing a balance out partway — for a renovation, or in a panic during a downturn — does not pause the curve; it restarts it at zero for every dollar withdrawn, and the years that money had already served were the cheap ones. Compounding rewards one behaviour above all others: leaving it alone. The deposits can be modest and the fund ordinary, so long as neither is disturbed.

Run your numbersCompound growth→

The rule of 72

Divide 72 by an annual growth rate and you get, near enough, the number of years a balance takes to double. It is the mental shortcut for everything above, and it is accurate enough to make real decisions with:

The approximation is tightest between roughly 4% and 12% and drifts a little outside that band, but its real value is chaining doublings. At 6%, money doubles about every twelve years, so a thirty-year horizon holds two and a half doublings — a factor of about 5.7, which is exactly why $10,000 became $57,435 in the first table. It also prices delay instantly: at 8%, starting nine years late costs a full doubling, meaning the entire final balance would have been twice as large.

Run it on inflation too. At 3% inflation, prices double roughly every 24 years — the same arithmetic, aimed at your cash. Money earning nothing is not standing still; it is compounding downward in purchasing power.

The same curve runs against you

A debt balance is a compound account owned by someone else. Everything above applies unchanged: interest is charged on the balance, unpaid interest joins the balance, and next month's interest is charged on the sum. At a typical credit card rate around 20%, the rule of 72 says an untouched balance doubles in under four years, with no new spending required. This is why minimum payments feel like running on ice — most of each payment is absorbed by the month's interest before the balance moves. How credit card interest works walks through the mechanics, and the credit card interest calculator prices a real balance in months and dollars.

Fees compound against you the same way, just more quietly. Two percentage points of annual cost sound like a small fraction of a 7% return; over thirty years they are the difference between $10,000 growing to $76,123 and growing to $43,219 — 43% of the final balance absorbed by a number that looked small every single year. The general rule: anything that shifts your rate a little, permanently, moves the destination a lot.

What to actually do

Three moves follow directly from the mechanism.

First, start now, at whatever amount survives contact with your budget. The two-saver arithmetic is indifferent to why the late starter was late: waiting for the perfect fund, the higher salary, or the end of the debate about what savings rate is good enough all cost the same years. Early on, the amount you save dwarfs what the return contributes anyway — the rate debate matters later, once there is a balance for the rate to act on.

Second, protect the rate you already have. Cash earning nothing while inflation compounds is a slow leak; park it where it earns a real rate — the savings interest calculator shows what a single point of difference does over time — and be ruthless about recurring fees, which the arithmetic above prices at far more than their sticker.

Third, aim the curve at something. Left abstract, compounding is a pleasant chart; pointed at a number, it becomes a plan with a date. Coast FIRE math is the cleanest example — finding the point where the balance you already hold will compound to retirement on its own, with no further deposits — and it is a direct application of everything on this page: once the doublings ahead of you are worth more than the deposits you could still make, the mechanism has taken over the job.