Compound interest calculator with monthly contributions
This calculator projects what a monthly contribution could be worth at a fixed annual return, with an optional yearly raise in the contribution and the effect of inflation. Below we explain exactly how it does the math, how much each assumption moves the result and what it cannot predict.
Compound interest calculator
How compound interest works with monthly contributions
Compound interest means earning returns on the returns you already earned. When you add money every month, two engines run at once: your contributions, which grow in a straight line, and your gains, which grow faster and faster because they are calculated on an ever larger balance.
Year 1: you contributed $2,400 and the balance is about $2,465. Gains are only $65.
Year 10: you contributed $24,000 and the balance is about $32,495 ($8,495 in gains).
Year 20: you contributed $48,000 and the balance is about $90,688 ($42,688 in gains).
Between years 10 and 20 you add the same amount as in the first ten, but gains grow fivefold.
That is why time matters so much: in the early years almost the whole balance is your own money, and the gains only become visible once the balance is large.
How the calculator does the math
So you can reproduce it in a spreadsheet, these are the exact assumptions:
- Equivalent monthly rate: the annual return is converted to a monthly one with (1 + annual rate)^(1/12) - 1. A 6% annual rate is 0.4868% a month, not 0.5%, so twelve months in a row give exactly 6% for the year.
- Initial amount: invested on day one and growing from the first month.
- Contributions at the end of each month: every month the balance grows at the monthly rate and then the contribution is added. A month’s contribution starts earning the following month.
- Annual increase: at the start of each new year (from year 2 on) the monthly contribution is multiplied by (1 + increase). With $200 and 3%, you add $206 a month in year 2, $212.18 in year 3, and so on.
- Value in today’s money: if you enter an inflation rate, each year’s value is divided by (1 + inflation)^years.
In one line: every month, balance = balance x (1 + monthly rate) + contribution. The yearly table shows total contributed, value, gains (value minus contributed) and value in today’s money.
Why raising your contribution each year matters
A fixed contribution loses purchasing power to inflation: $200 fifteen years from now will not buy what it buys today. Raising it a little every year, in line with your salary or with inflation, keeps your real effort constant and changes the outcome noticeably.
No increase: you contribute $48,000 in total and the balance reaches about $90,688.
With a 3% yearly increase: the last year’s contribution is about $350.70 a month, you contribute about $64,489 in total and the balance reaches about $115,132.
The gap, about $24,444, comes from contributing more and from those extra contributions compounding too.
Nominal value and real (inflation-adjusted) value
Nominal value is the dollar figure in that future year. Real value is what that figure would buy at today’s prices. With inflation, the second is always lower.
Over 20 years, prices rise 80.6%: 1.03^20 is about 1.806.
Real value: 90,688 / 1.806 is about $50,212 in today’s money.
With the contribution rising 3% a year: 115,132 / 1.806 is about $63,746 in today’s money.
Keep the return and the inflation rate in the same currency. If you project in dollars, use dollar inflation; if you think in euros, pounds or another currency, the expected return and the inflation should both be in that currency, because the exchange rate in between matters too.
How much the return assumption changes the result
Two percentage points either way sound small, but over 20 years they move tens of thousands of dollars. These figures use exactly the method above, with no initial amount:
| Annual return | Contributed | Value after 20 years | Gains | Value with 3% yearly increase |
|---|---|---|---|---|
| 4% | $48,000 | about $72,768 | about $24,768 | about $94,085 |
| 6% | $48,000 | about $90,688 | about $42,688 | about $115,132 |
| 8% | $48,000 | about $113,800 | about $65,800 | about $141,987 |
Going from 4% to 8% does not double the final balance (it rises 56%), but it multiplies the gains by more than 2.5. That is why it helps to try several scenarios rather than one.
The limits of the model
The calculator assumes a constant return. Markets do not behave that way, and it has consequences:
Returns are not constant
A 6% average can be +25% one year and -15% the next. With regular contributions, the order matters as well: a drop hurts more when the balance is large.
$200 a month for 20 years, 6% every year except one year at -30%.
If the drop comes in year 2: the final balance is about $86,966.
If it comes in year 20: the final balance is about $60,309.
No drop: about $90,688. Same returns, different order, a gap of about $26,657.
Fees and taxes
A 1% yearly fee or fund expense ratio turns a 6% return into 5%: in the example, the 20-year balance falls from about $90,688 to about $81,161. Taxes on dividends and sales also take their share, and dividend withholding depends on where you live; the dividend withholding calculator gives you an idea of that part. Tax rules vary, so check your own case with your broker or a tax advisor.
Your actual return is measured differently
The return you enter here is an assumed rate. The one you actually get, with contributions on irregular dates, is measured with XIRR (money-weighted) or TWR (time-weighted). This guide explains the difference and why your broker may show you another number.
An illustration, not a promise
The result depends entirely on the assumptions you type in. Nobody can guarantee a return, and an index’s past does not secure its future. The calculator helps you understand the effect of time, contributions and inflation and compare scenarios, not know how much you will have.
To compare a projection with where you actually are, you need your real transactions in one place: a spreadsheet works (what to include and where it breaks), and so does a portfolio tracker that calculates your XIRR and TWR across all your brokers.
Frequently asked questions
Why isn't the monthly rate the annual rate divided by 12?
Because returns compound month by month. 0.5% a month for 12 months gives 6.17% a year. The equivalent rate, (1 + 6%)^(1/12) - 1, about 0.4868%, gives exactly 6% by the end of the year.
Are contributions made at the start or the end of the month?
At the end of each month: the balance first grows at the monthly rate and then the contribution is added. The initial amount, on the other hand, is invested from day one.
Which inflation rate should I use?
The one for the currency you project in. If you calculate in dollars, use dollar inflation; if you calculate in your local currency, use your country’s, with an expected return in that currency too.
What return should I enter?
There is no correct figure: the calculator does not predict returns. What helps is trying several scenarios, for example a cautious one and an optimistic one, and seeing how much the result changes.
By Asterholm TeamUpdated:
Educational content, not investment or tax advice. Rules, fees and rates change: check with your broker or an advisor. Risk notice.
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