Continuous Compound Interest Calculator

What this calculator projects

Compounding is the quiet engine behind growing money. You earn interest, then you earn interest on that interest, and given enough time the curve starts to bend upward in a way that surprises people. This calculator shows you that curve at its theoretical fastest, using continuous compounding, where the interest is imagined to pile on at every possible instant.

Give it a starting balance, a rate, and a stretch of time, and it tells you what you would end with and how much of that is pure interest. If you plan to keep adding money along the way, it handles that too, including deposits that grow a little each year.

How to use it

Start with the basics: your initial balance, the interest rate, and the term, which you can set in years and months together.

If you are only growing a single lump sum, leave the deposits option on "Never" and you are done. If you plan to keep contributing, pick how often under Additional Deposits, then enter how much each time, whether it lands at the beginning or end of each period, and an optional annual growth rate for those deposits if you expect to raise them over time. That last touch is handy if you plan to save a bit more each year as your income grows.

What you get back

For a single lump sum, it gives you the final balance and the compounded interest that got you there.

Once you add regular deposits, it breaks the picture down further, so you can see it clearly: your total deposits, the interest earned on those deposits, and the interest on your starting balance, all adding up to the final figure. Splitting it out like that shows you how much of your ending balance you put in yourself, and how much the compounding did for you.

The formula doing the work

At the centre is one of the most elegant equations in finance:

A = P × ert

Here P is your starting balance, r is the rate, t is the time in years, and e is a special number, roughly 2.71828, that shows up naturally whenever something grows continuously. The tool works out t from your years and months, runs that formula for your starting balance, and then, if you added deposits, applies the same continuous growth to each deposit for however long it sits in the account before the end. Add it all together and you have your final balance.

A worked example

Say you start with 10,000, earn 6 percent, and leave it for 10 years with no further deposits.

The tool grows it to about 18,221, meaning roughly 8,221 of that is interest. Your money nearly doubled without you lifting a finger. For a sense of what the "continuous" part adds, the very same money at 6 percent compounded once a year would reach about 17,908. So the fastest possible compounding buys you around 313 extra over a decade, real but modest, which is a useful thing to see with your own eyes.

A word on "continuous"

It is worth being straight with you about what continuous compounding is. It is the mathematical ceiling of compounding, what you get if interest is added not yearly, not daily, but at every instant. No bank actually pays interest this way. It lives mostly in finance theory and in the models that price bonds and options.

So why use it? Because it gives you the cleanest, upper-limit view of how a rate can grow money over time. And here is the reassuring part: the most frequent compounding you will meet in real life, daily, lands almost exactly on the continuous figure anyway, usually within pennies. If you want the everyday version that real savings accounts use, the Daily Compound Interest Calculator is the one to reach for.

Questions people ask

What does continuous compounding mean?

It is compounding taken to its limit, with interest added at every possible moment rather than at set intervals. It produces the highest result any given rate can reach, which is why it is used as a theoretical benchmark.

Does any bank actually pay this?

No. Real accounts compound daily, monthly, or yearly. Continuous compounding is a finance and math concept. That said, daily compounding comes so close that the difference is usually a matter of pennies.

What is that number e?

It is a constant, about 2.71828, that turns up naturally in continuous growth. Think of it as the number the compound interest formula settles on when you let the compounding happen infinitely often.

Can I include money I add regularly?

Yes. Switch the deposits option away from "Never," and set how often, how much, and when. You can even give those deposits a yearly growth rate if you plan to save more as time goes on.

References

The formula is the standard continuous compounding equation from financial mathematics.

1. U.S. Securities and Exchange Commission, Investor.gov. Compound interest and how savings grow. https://www.investor.gov/financial-tools-calculators/calculators/compound-interest-calculator
2. Broverman, S. A. Mathematics of Investment and Credit (compound interest and continuous compounding). ACTEX Publications.