Start with $10,000, add $250 a month, and assume 7 per cent a year compounded monthly. In year eight the account earns $3,228 while you pay in $3,000 — the first year growth beats contributions. In year sixteen the cumulative interest passes the cumulative amount you have added. After twenty years the balance is $170,619, of which $70,000 is yours and $100,619 is growth.
Those two crossovers are the whole argument for starting early, and they are far apart. Knowing which one a piece of advice is talking about explains most of the disagreement about how long compounding takes to matter.
What do the two crossovers look like?
The first is annual: the year the interest earned exceeds the money added. The second is cumulative: the year total interest overtakes total contributions.
| Year | Added | Interest that year | Balance | Total added | Total interest |
|---|---|---|---|---|---|
| 1 | $3,000 | $821 | $13,821 | $13,000 | $821 |
| 5 | $3,000 | $2,052 | $32,074 | $25,000 | $7,074 |
| 8 | $3,000 | $3,228 | $49,528 | $34,000 | $15,528 |
| 12 | $3,000 | $5,234 | $79,281 | $46,000 | $33,281 |
| 16 | $3,000 | $7,886 | $118,616 | $58,000 | $60,616 |
| 20 | $3,000 | $11,392 | $170,619 | $70,000 | $100,619 |
Year eight is the annual crossover. Year sixteen is the cumulative one. In the first seven years the plan is essentially a savings account with a small bonus; from year sixteen the rate matters more than anything you do.
Why is nothing happening in the early years?
Because interest is charged on a balance that is mostly what you just deposited. In year one the account earns $821 on an average balance of about $12,000 — real money, and invisible next to the $3,000 you added.
This is the phase where people conclude that compounding is oversold. It is not; it is back-loaded. The same $3,000 a year buys $821 of growth in year one and $11,392 in year twenty, and nothing about the plan changed except how long it had been running.
It is also why the first few years are the ones people abandon. Nothing in the table between years one and five suggests what year twenty looks like, and the account gives no signal at the point where stopping is most costly.
What does the frequency of compounding add?
Less than most people expect. Ten thousand at 7 per cent for ten years, with nothing added:
| Interest added | Final balance |
|---|---|
| Yearly | $19,671.51 |
| Quarterly | $20,015.97 |
| Monthly | $20,096.61 |
| Daily | $20,136.18 |
The whole spread from yearly to daily is $464.67 across a decade, or 2.4 per cent of the final balance. Moving from yearly to monthly captures most of it; the step from monthly to daily is worth $39.57. Frequency is worth understanding and is not worth choosing a product for.
What does inflation do to the same figures?
It changes what the number means without changing the number. That $170,619 after twenty years, deflated at 2.5 per cent a year, has the buying power of $104,124 today — the growth is real, and it is about 39 per cent smaller than the headline suggests.
The useful habit is to run the projection twice: once nominally, to know what the statement will say, and once in today’s money, to know what it will buy. The second figure is the one to make decisions against, and it is the one people quote least often.
Does the starting amount or the monthly contribution matter more?
Early on, the contribution. Later, whatever has been compounding longest. In this plan the $10,000 opening balance grows to $40,387.39 over twenty years at 7 per cent, while the $60,000 of contributions grows to $130,231.66 — but the contributions had an average of ten years to work and the opening balance had twenty.
Per dollar, the early money wins comfortably. Per decision, the monthly contribution usually wins, because it is the one you can still change.
Questions people ask
Should contributions go in at the start or the end of the month? The start, by a small margin — each contribution earns one extra month of interest. Over twenty years at these numbers it is worth $759.68, or about 0.4 per cent of the final balance.
What rate should I assume? Something you can defend, and then test either side of it. A projection at a single rate is a story; the same projection at two rates is a range.
Does this account for tax? No. Growth inside a tax-sheltered account and growth in a taxable one behave very differently, and the difference compounds along with everything else.
Why does my provider’s projection differ? Usually charges. An annual management fee comes off the return before compounding, so a 7 per cent gross return with a 1 per cent fee compounds at 6 per cent — which on this plan ends at $148,612.27 instead of $170,619.05. The fee is 1 per cent and it costs 12.9 per cent of the outcome.
Does the crossover year move much with the rate? Yes, and more than the final balance suggests. A lower return pushes both crossovers later, because the interest has to climb further to catch a contribution that has not changed.
What if I stop contributing? The balance keeps compounding on what is there. After the annual crossover in year eight, the account is already adding more each year than you are, so stopping slows the plan without stalling it.
Two crossovers, twelve years apart, and the second one is where the plan stops depending on you. The compound interest calculator shows the year-by-year split, the retirement calculator runs the same maths to a target age, and the inflation calculator converts any of it into today’s money.