When your interest overtakes your deposits
Your data
The return is a field rather than a number written into the page, because any figure fixed here would be this page taking a position on the future. Put in what you actually expect, and try a worse one afterwards.
The monthly deposit is treated as arriving at the end of the month, so it earns nothing in the month it is made, and the yearly rate is converted by compounding rather than by dividing by twelve.
Results
Years before one month of interest is worth more than one month of your money
—
| The balance at which that happens, whatever route got you there | — |
| Monthly rate the yearly one really means, in percent | — |
| What you end up with | — |
| How much of that you put in yourself | — |
| How much of it the money made on its own | — |
| Share of the end result that is interest, in percent | — |
| What the monthly deposit would have to be if you started five years later | — |
Who is building the pile, year by year
| Year | Balance | Of that, yours | Of that, interest | Interest as a share, in percent |
|---|
Read the last column downwards and you have the whole argument. At a thousand a month and ten per cent a year, interest is four in a hundred of the balance after one year, twenty two after five, forty after ten and eighty two after thirty. Anyone who gives up in year three gives up during the stretch where the arithmetic has not started yet.
The crossing is a balance and not a date, which is the part worth carrying away. One month of interest is the balance times the monthly rate, and one month of deposits is just the deposit, so the two are equal exactly when the balance equals the deposit divided by the rate. Reaching that number by inheriting it, by selling something or by saving for eight years makes no difference at all to what happens afterwards.
This is also why starting late costs more than saving little. Someone who puts aside five hundred a month for thirty five years ends with more than someone who puts aside a thousand for twenty five, and does it while paying in ninety thousand less. To draw level, the one who starts ten years later has to find nearly three times the monthly deposit, which is a different kind of problem from being patient.
None of this is advice about where to put the money, and the return you typed is an assumption rather than a promise. What the page can honestly tell you is the shape: slow while you carry it, then increasingly carried for you, and the date on which that changes hands.
When does interest start earning more than I put in?
At a thousand a month and ten per cent a year, starting from nothing, it takes eighty nine months, which is about seven and a half years. Before that the pile is mostly your own money.
The important part is that the trigger is a balance rather than a date. One month of interest is the balance times the monthly rate, and one month of deposits is the deposit, so they are equal when the balance equals the deposit divided by the rate. In that example it is 125,405, and it makes no difference whether you saved it, inherited it or sold something to get there.
Why is almost all of my balance still my own money?
Because that is the shape of the thing early on. At a thousand a month and ten per cent a year, interest is four per cent of the balance after one year, twenty two per cent after five and forty per cent after ten. It passes half somewhere around year fourteen.
It is worth knowing before you start rather than after, because the years that feel pointless are the ones the later years are built on.
| Year | Balance | Of that, interest | Interest as a share |
|---|---|---|---|
| 1 | 12541 | 541 | 4.3% |
| 5 | 76561 | 16561 | 21.6% |
| 10 | 199864 | 79864 | 40.0% |
| 20 | 718259 | 478259 | 66.6% |
| 30 | 2062843 | 1702843 | 82.5% |
Is it better to save more or to start earlier?
Earlier, and by a wide margin. Someone putting aside five hundred a month for thirty five years ends with about 1,699,000, while someone putting aside a thousand a month for twenty five years ends with about 1,233,000. The first pays in ninety thousand less and finishes with four hundred and sixty six thousand more.
To draw level, the one who starts ten years later would need about 1,378 a month, which is nearly three times the original deposit. That is the honest way to price a delay: not in years, but in what the deposit would have to become.
| Plan | Paid in | Ends with |
|---|---|---|
| 500 a month for 35 years | 210000 | 1699396 |
| 1000 a month for 25 years | 300000 | 1233325 |
Why divide the yearly rate by compounding instead of by twelve?
Because dividing by twelve is the proportional rate, which only behaves that way under simple interest. Ten per cent a year divided by twelve is 0.8333 per cent a month, and that compounded twelve times comes back as 10.47 per cent a year, so the calculation contradicts itself.
The equivalent rate is the twelfth root instead, which for ten per cent a year is 0.797414 per cent a month. Over thirty years the difference between the two is not a rounding detail.
What return should I assume?
That is the one thing this page will not answer for you, which is why it is a field and not a number written into the code. Any figure fixed here would be the page taking a position on the future.
The useful habit is to run it twice: once with the return you expect and once with a return you would be unhappy about. If the plan only works on the optimistic one, that is worth knowing now.
Does this page tell me where to invest?
No. It does arithmetic on the assumptions you type, and where the money goes is a decision with more in it than arithmetic.
What it can tell you honestly is the shape of the climb: slow while you are the one carrying it, then increasingly carried for you, and roughly when that changes hands.
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