Interest at work
Compound interest is the same mechanism in both directions: it grows a sum set aside, and it swells a debt left to run. Change the length of time, and watch what time builds on its own.
Everything is worked out in your browser. No amount leaves your device, nothing is saved, and the Clear button empties everything. How to check it.
Enter a sum or a monthly payment in, a rate and a length of time: the result appears here.
One of the boxes does not hold a readable number, and it is flagged. Spaces, commas and full stops are accepted.
One of the boxes holds a perfectly readable number that describes no real situation, and it is flagged. For instance a negative starting sum or monthly payment, or a term shorter than one month.
| Value at the end | |
|---|---|
| Sum actually paid in | |
| What the interest added | |
| Share of the total made up of interest | % |
| The sum paid in is multiplied by | |
| Time to double, rule of 72 | years |
This table was worked out by compounding the interest once a year, the default setting. Its formula is further down.
This table was worked out by compounding the interest every month. Its formula is further down.
The same result reads two ways. If this is your savings, the interest added is yours. If it is a debt you are not repaying, it is what you will owe on top.
The method
This calculator applies a single formula, under whichever compounding you pick above. Compounding once a year is the default setting: it is the one that gives the figures the course teaches.
Compounding once a year, the default setting
value = capital × (1 + annual rate) to the power of the number of years, plus annual payment in × ((1 + annual rate) to the power of the number of years, minus 1) divided by the annual rate.
- The annual rate is the one you type in, untouched, and the number of years is the length of time you type in. A sum of 1,000 at 10% a year therefore gives 1,100 after one year, 1,210 after two years and 2,594 after ten years: the very figures of the course.
- The annual payment in is your monthly payment multiplied by twelve. The twelve payments of one year are counted together at the end of that year: they only earn from the following year onwards, so the result understates rather than overstates.
Compounding every month
value = capital × (1 + monthly rate) to the power of the number of months, plus payment in × ((1 + monthly rate) to the power of the number of months, minus 1) divided by the monthly rate.
- The monthly rate is the annual rate divided by twelve: the rate you type in is therefore treated as a nominal rate, exactly like the borrowing rate on the credit page. A rate of 12% thus grows a sum by 12.68% in one year, because one month’s interest earns interest the next month.
What holds in both cases
- The first term puts what you already have to work, the second puts what you add to work.
- When the rate is zero, only the sum paid in remains: capital plus payment in multiplied by the number of months.
The rule of 72, the one that sticks
Divide 72 by the annual rate: you get the number of years a sum takes to double. At 6%, twelve years. At 2%, thirty-six years. At 12%, six years. It is not exact to the last decimal, and that is precisely what makes it useful: it works in your head, in the middle of a conversation, with no phone.
It also serves to spot the impossible. A return advertised at 60% a year would double a sum in a little over a year, 72 divided by 60, so it would multiply it by more than a hundred in ten years. That is the test our Testing a promised return page runs.
Why this page exists
According to the OECD international survey of adult financial literacy, recorded in 2022-2023 across 39 countries and economies, only 42% of adults answer a question on compound interest correctly, and 63% are able to apply the value of time to their own savings. It is not a question of ability: it is an idea that is taught almost nowhere, and that decides a great deal.
What this tool does not do
- It predicts nothing: a past rate is not a future rate, and no return is guaranteed.
- It takes account of neither inflation nor tax, which depend on the country and the year.
- It recommends no investment and names none.
Read next: compound interest, inflation, risk. To understand the other direction of the same mechanism, move on to the cost of a loan.