Compound interest: what actually matters
Compound interest has four inputs — a starting amount, a regular contribution, a rate and a length of time — plus a fifth that everybody asks about and almost nobody should: how often it compounds.
The four that matter do not matter equally, and the ranking is not obvious. Here is what each one is actually worth.
The crossover is the whole point
Start with $10,000, add $500 a month, assume 7% a year, and after twenty years you have $300,850.72. You put in $130,000 of that. The other $170,850.72 is growth.
That crossover — the moment the account has made more than you have paid in — is what compounding is for, and it is the reason time outranks everything else. It does not arrive gently; it arrives late and then dominates.
Run the same numbers without the monthly contributions and the $10,000 alone becomes $40,387.39. Useful, but it is the contributions doing the heavy lifting. Compounding multiplies what you feed it, and it cannot multiply nothing.
$10,000 start, $500/month, 7%, 20 years
Final balance $300,850.72
You put in $130,000.00
Growth $170,850.72
Same, no contributions: $40,387.39
Work it out: Compound Interest Calculator →
Compounding frequency is the least important input
This is the question that gets asked most and deserves it least. Take the example above and switch it from monthly compounding to annual: the balance goes from $300,850.72 to $284,669.80.
That is a difference of about five per cent over twenty years — real, but far smaller than a single percentage point on the rate, and utterly dwarfed by the contributions. Anyone choosing between two accounts on compounding frequency is optimising the wrong variable.
The reason it matters so little is that the gain from more frequent compounding is bounded. Going from annual to monthly captures most of it; going from monthly to daily captures almost nothing, and going to continuous compounding — the mathematical limit — barely moves it again.
A steady rate is a convenience, not a forecast
Every compound interest calculation assumes the same return every year, and no investment behaves that way. The result is a projection of what a smooth version of the world would produce, which is useful for comparing plans and misleading if read as a prediction.
Two things follow. First, the further out the projection runs, the more the assumed rate dominates the answer, so a thirty-year figure is really a statement about the rate you guessed. Second, the order of returns matters in real life and not at all in the model — the same average with the bad years at the start leaves you meaningfully worse off when you are drawing money out.
Treat the number as a way of comparing "save $400" against "save $600", not as a balance you will one day see.
Working backwards from a goal
The more useful direction is usually the reverse: given a target and a date, what does it take each month? To reach $50,000 in five years starting from $5,000 at 5%, the answer is $640.87 a month.
Of that $50,000, you contribute $38,452.33 and growth supplies $6,547.67. Over five years compounding is a helpful assistant rather than the main character — which is exactly the point about time. The same maths over twenty years has growth doing most of the work.
Missing months matter more at the beginning than the end, because early money has the longest to compound. Catching up later costs more than keeping up now.
Work it out: Savings Goal Calculator →
CAGR describes the trip, not the ride
When you already know what something did, the compound annual growth rate turns it into a comparable figure. $10,000 becoming $32,000 over twelve years is a 10.18% annual return — a total return of 220%, or 3.2 times the money, doubling roughly every seven years and two months.
What CAGR is not is a description of what happened. It is the steady rate that would have produced the same result, and real returns are lumpy. Two investments with identical CAGRs can differ enormously in how far they fell along the way, and the falls are what people actually experience.
It also ignores money paid in or taken out. For an account you have been contributing to, the CAGR of the balance is not your return — it is your return mixed together with your saving, and it flatters the first.
Work it out: CAGR Calculator →
Questions
Does compounding frequency make much difference?
Very little. Over twenty years, switching the same plan from annual to monthly compounding changed the balance by about five per cent — less than one point on the rate, and nothing beside the contributions.
What matters most in compound interest?
Time first, then how much you contribute, then the rate, and compounding frequency a distant last. Time is the only one that multiplies the effect of the others.
When does the growth overtake what I put in?
On $500 a month at 7% from a $10,000 start, growth exceeds contributions within twenty years — $170,851 of growth against $130,000 paid in. It arrives late and then dominates.
Is a compound interest projection reliable?
As a comparison between plans, yes. As a prediction, no — it assumes an identical return every year, and the longer the projection the more the whole answer rests on the rate you assumed.
What is CAGR?
The steady annual rate that would have taken a starting value to an ending one. It is a way of comparing results, not a description of the path — two investments with the same CAGR can have felt completely different.
Can I use CAGR on my savings account balance?
Not meaningfully, if you have been paying into it. CAGR of the balance mixes your contributions in with the return and makes the return look far better than it was.