Compound Interest Calculator

How compound interest works

Compound interest is interest that earns interest. Once a period's interest is added to your balance, the next period's interest is worked out on the bigger number, so the growth speeds up as it goes.

Three things drive it: the amount you start with, the rate, and how long you leave it. The rate is quoted per year, but interest is usually added more often than once a year, so the calculation works on a periodic rate rather than the annual one.

The formula

B = P x (1 + i) to the power of N

• B is the balance at the end.
• P is the amount you start with.
• i is the periodic rate, which is the annual rate divided by the number of times interest is added each year.
• N is the total number of periods, which is the number of times per year multiplied by the number of years.

Read it as one sentence: take what you started with, and multiply it by "one plus the periodic rate" once for every period that goes by.

Why time does more work than the rate

Time sits in the exponent. The rate only changes the size of each step, but time changes how many steps there are, and every step is applied to the result of the last one. That is why the curve steepens instead of climbing in a straight line.

If you assume a 5 percent annual rate on a starting amount of $10,000, compounded once a year and left alone, the interest earned is $6,288.95 after ten years, $16,532.98 after twenty, and $33,219.42 after thirty. The money did not work harder in the third decade. It just had more to work on.

How often interest compounds, and why it matters

Two accounts can advertise the same rate and not pay the same amount. The difference is how often the interest is added. Add it more often and each addition is smaller, but it starts earning sooner, so the year ends slightly ahead.

The table below assumes a starting amount of $10,000 and a 5 percent nominal rate held for ten years. The 5 percent is an assumption chosen to make the comparison readable. It is not a rate this page suggests, expects or endorses, and the calculator will use whatever rate you enter instead.

Moving from annual to daily compounding takes the balance from $16,289 to $16,487 on this fixture. That is real, and it is worth knowing when you are comparing two products. It is also much smaller than the effect of changing the rate or the number of years, which is the more useful thing to notice.

There is a ceiling to this. As you add interest more and more often, the yearly total keeps rising but by less and less each time, and it approaches a limit rather than running away. Mathematicians call that limit continuous compounding. This calculator explains it but does not offer it as an option, because no ordinary account pays that way and offering it would invite a comparison nobody can act on.

Nominal rate versus effective rate (APR and APY)

The quick answer: the nominal rate is the number on the label, and the effective rate is what you actually end up with once compounding is counted.

The effective annual rate, usually shown as APY, is what a year of compounding actually delivers:

APY = (1 + r divided by n) to the power of n, minus 1

• r is the nominal annual rate.
• n is how many times a year interest is added.

If you assume a 5 percent nominal rate, the effective annual rate is 5.00 percent when interest is added once a year, 5.12 percent when it is added monthly, and 5.13 percent when it is added daily. Same label, three different products.

This is why comparing two headline rates is not enough on its own. Compare the effective rates, or compare the balances after the same number of years, which is what the calculator above does for you. The same distinction exists when you are borrowing rather than saving, and it moves in the opposite direction: more frequent compounding on a debt works against you.

Adding regular contributions

The quick answer: a starting amount and a stream of contributions are two separate calculations added together.

Your starting amount compounds for the whole period. Each contribution only compounds for the time left after it arrives, so the first one you ever make does far more work than the last one. Add the two results together and you have the balance.

The formula for the contribution stream

FV = PMT x (((1 + i) to the power of N) minus 1) divided by i

• PMT is the amount you put in each period.
• i is the periodic rate.
• N is the number of periods.

When the rate is zero, that formula divides by zero, so it degenerates to the obvious answer: FV = PMT x N. The calculator handles that case directly rather than treating it as an error.

What it looks like

Starting from nothing, putting in $500 a month, assuming a 7 percent annual rate compounded monthly, over 30 years, the calculator returns a balance of $609,985.50. Of that, $180,000.00 is money you put in and $429,985.50 is interest.

That split is the part worth staring at. The headline number hides it, and the headline number is not the interesting part.

When contributions land: end of period

This calculator adds contributions at the end of each contribution period, and it credits interest at the end of each compounding period on the balance that was standing at the start of it. There is no start-of-period option.

That has a consequence you should know about before you trust a number.

Interest here is added at the end of each compounding period, so money you pay in partway through that period starts earning at the next compounding date rather than on the day it lands. One practical effect: putting in $500 twice a month gives the same answer here as putting in $1,000 once a month. Run both on a $10,000 starting amount at an assumed 6 percent compounded monthly for ten years and you get $182,073.31 either way. In real life the twice-a-month saver would come out slightly ahead, because half the money is invested about two weeks earlier. This calculator does not model that small difference, so if anything it is slightly conservative.

The same thing applies to biweekly contributions against monthly ones, and to any arrangement where you pay in more often than interest is credited.

If your own account pays interest from the day money lands, or you contribute at the start of each period rather than the end, your real figure will be a little higher than the one shown here. Not a lot higher, but higher.

Reading your results: interest versus what you put in

The balance is what your starting amount plus your contributions become if your assumptions hold for the whole period. The interest figure beside it is the part you did not put in yourself. That second number is the one to watch.

On the values the calculator loads with, a $5,000 start, $250 a month, an assumed 6 percent compounded monthly, over 20 years, the balance is $132,061.25. Of that, $65,000.00 is money you put in and $67,061.25 is interest. The interest has just overtaken the contributions. Where that crossover happens, and how far past it you get, is the whole story of a long horizon.

How to use the calculator rather than just read it

Change one input at a time and watch the interest card, not the balance card. The balance always goes up when you feed it more, which tells you nothing. The interest tells you which lever actually did the work.

From those same starting values, stretching the horizon from 20 years to 25 takes the balance to $195,573.34, with $115,573.34 of it interest. Raising the monthly contribution from $250 to $300 and leaving everything else alone gives $155,163.29, with $78,163.29 of it interest. Five more years did more than an extra $50 a month, because time compounds and a bigger deposit does not.

Two other things worth trying. Run the same rate at annual compounding and then at daily, and watch how little moves, so you stop over-weighting that choice. And if the money is going into a business rather than into an account, the growth question is a different one, and our Business Loan ROI Calculator is the tool for it.

What your balance is worth in today's dollars

A balance thirty years out is quoted in future money, and future money buys less. If you want the figure in today's money, enter your own inflation assumption and the calculator will deflate the result:

Today's dollars = balance divided by ((1 + your inflation assumption) to the power of years)

Using the values the calculator loads with and adding a 2.5 percent inflation assumption, the $132,061.25 balance becomes $80,593.14 in today's dollars.

Three things to be clear about. The inflation rate is entirely your assumption. This page does not supply one, does not suggest one, and has no view on what it should be. Leave the field blank and the today's-dollars figure is not shown at all, rather than quietly defaulting to zero. And the deflator is applied once, at the end, to the final balance. It is not applied to each year of the trajectory.

Common mistakes

Reading a nominal rate as if it were the effective one. At an assumed 5 percent, the effective annual rate is 5.00 percent compounded annually and 5.13 percent compounded daily. If you compare one product's nominal rate against another's effective rate you will pick the wrong one. This trips people up on the borrowing side too, where the same arithmetic runs against you rather than for you, and our Mortgage Calculator shows what that looks like over a loan term.

Treating a fixed rate as a forecast. The calculator holds your rate constant for the whole period because it has to hold something constant. Real returns move around. What you get here is a projection from an assumption, not a prediction, and the further out you push it the more that matters.

Expecting the year-by-year table to hand-sum to the total. The figures shown are rounded to two decimal places while the calculation runs at full precision. Adding up what you see on screen can land a few cents away from the total. That is expected and it is not an error.

Assuming more frequent contributions always beat fewer larger ones. In this calculator they do not, because contributions start earning at the next compounding date rather than on the day they land. See the section on when contributions land for what that means and why the result here is slightly conservative.

Reading an input maximum as a suggestion. The largest values the form accepts are validation limits. They exist to stop nonsense input and to bound the arithmetic. They are not typical figures, not recommendations and not a claim that any of them is achievable.

Worked examples

Example A: a lump sum, and what compounding frequency actually did

The question. You have $10,000, you are assuming a 5 percent annual rate, and you want to leave it for ten years. How much does compounding frequency change the answer?

Step 1: find the periodic rate. Interest is added monthly, so the periodic rate is the annual rate divided by 12.

Step 2: count the periods. Twelve periods a year for ten years is 120 periods.

Step 3: apply the formula. B = 10,000 x (1 + i) to the power of 120.

Step 4: read the result. The calculator returns a balance of $16,470.09. Money in was $10,000.00, so $6,470.09 of that is interest. The effective annual rate is 5.12 percent.

Step 5: change one thing. Switch compounding from monthly to annually and leave every other input alone. Now the periodic rate is the full 5 percent and there are 10 periods instead of 120. The calculator returns $16,288.95, of which $6,288.95 is interest, at an effective annual rate of 5.00 percent.

What it shows. Same money, same stated rate, same ten years. The only difference was how often the interest was added, and that is exactly the gap between a nominal rate and an effective one.

Example B: starting from nothing, with contributions

The question. You have nothing set aside. You can put in $500 a month, you are assuming a 7 percent annual rate compounded monthly, and you want to know what 30 years of that looks like.

Step 1: the starting amount is zero. There is no lump sum compounding here. Everything in the answer comes from the contributions and what they earn.

Step 2: count the contribution periods. Twelve a year for 30 years is 360 contributions.

Step 3: add up what you put in. 360 contributions of $500 is $180,000.00. The calculator reports exactly that as total money in.

Step 4: apply the contribution formula. FV = 500 x (((1 + i) to the power of 360) minus 1) divided by i, where i is the 7 percent annual rate divided by 12.

Step 5: read the result. The calculator returns a balance of $609,985.50, of which $180,000.00 is contributions and $429,985.50 is interest.

What it shows. Interest is more than twice what you put in, and none of it came from a large starting amount, because there was not one. It came from 360 small contributions and 30 years. The first contribution compounded for the entire period. The last one compounded for a month.

Both examples state their rate as an assumption. Neither rate is a suggestion, a historical figure, or a claim about what any account pays.

Advanced and edge cases

Continuous compounding, and why it is not an option here. Add interest more and more often and the yearly total keeps rising, but by smaller and smaller amounts, approaching a ceiling rather than growing without bound. That ceiling is continuous compounding. It is the theoretical top end of the frequency question and it is worth understanding, which is why it is explained here. It is not offered as a choice because no ordinary account pays that way, and offering it would produce a comparison you cannot act on.

Partial periods, and how they are handled. The years input accepts one decimal place, so at almost every frequency the last compounding period is incomplete. That final stub earns interest by simple proration: a half period earns half a period's interest. It does not compound fractionally. The distinction is small but it is a deliberate choice, not an accident. Worked through: $1,000 at an assumed 7 percent, compounded annually, for 1.5 years returns $1,107.45. One full year of interest, then half a year's worth applied straight.

Contributions in an incomplete period do not count. A contribution happens at the end of a contribution period, so a period that never finishes never produces one. With a $10,000 start, $300 a month, an assumed 6 percent compounded monthly, over 10.6 years, twelve monthly periods across 10.6 years works out to 127.2, which means 127 completed contributions totalling $38,100.00 and a balance of $71,954.60. The 0.2 of a period is not rounded up into a payment that was never made.

There is no calendar. Every period here is an exact fraction of a year. Biweekly is one twenty-sixth of a year, which is about 14.04 days rather than exactly 14. Semi-monthly is one twenty-fourth, monthly is one twelfth, and daily compounding is one three-hundred-and-sixty-fifth. Leap years are not modelled and no period lines up with a real date. The trade is deliberate: it means a biweekly contributor gets exactly 26 contributions a year, which is what people expect from 26 pay periods, and it means the answer does not change depending on which day you happen to run the calculator.

A zero rate computes, it does not error. Put in 0 for the rate and the calculator does the sensible thing. A $5,000 start plus $250 a month for ten years at 0 percent returns $35,000.00, with $0.00 of interest. That is a real answer, not an error message.

Displayed rounding will not hand-sum. Every figure on screen is rounded to two decimal places while the calculation runs at full precision. Adding up the year-by-year balances can differ from the total by a few cents. That is expected.

The input maximums are limits, not suggestions. The form accepts up to $10,000,000 as a starting amount, $100,000 per contribution period, a 30 percent rate, 50 years, and a 20 percent inflation assumption. Those numbers exist to reject nonsense input and to keep the arithmetic well behaved. None of them is presented as normal, expected, recommended or achievable.

Very large results. Above a result of $10,000,000,000 the displayed figures may not be exact to the cent, because of how computers store very large numbers. The formulas are exact at every size; only the last cent of the display is affected.

What this calculator deliberately leaves out. Taxes of any kind. Fees, expense ratios, platform charges and spreads. Rates that change over time. Withdrawals. Contributions that go up over time. Currency conversion. And any product-specific rule such as contribution caps, employer matching, vesting or early-withdrawal penalties, which belong to dedicated tools rather than to a general compound interest calculator.

Frequently Asked Questions

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Important disclaimer

What this calculator assumes

Contributions are made at the end of each contribution period. Interest for a compounding period is credited on the balance standing at the start of that period, so money paid in during a period begins earning at the next compounding date. Your rate is held constant for the whole period. Your contribution amount is held constant, with no increases over time. There is no calendar and no start date: every period is an exact fraction of a year, biweekly being one twenty-sixth, semi-monthly one twenty-fourth, monthly one twelfth, and daily compounding one three-hundred-and-sixty-fifth, with leap years not modelled. A final incomplete compounding period earns interest by simple proration, and no contribution is made in a contribution period that does not finish. Every rate on this page, including the values the calculator loads with, is an assumption for illustration. Nothing here is a historical, typical, expected or recommended rate. The input maximums are validation limits only and are not suggestions.

What it does not account for

Taxes of any kind. Fees, expense ratios, platform charges and spreads. Variable or tiered rates. Withdrawals. Changing contribution amounts. Currency conversion. Product-specific rules such as contribution caps, employer matching, vesting or early-withdrawal penalties.

On rounding

Displayed figures are rounded to two decimal places while the calculation runs at full precision. Hand-summing the displayed year-by-year values can differ from the full-precision total by a few cents. That is expected and it is not an error. Above a result of $10,000,000,000 the displayed figures may not be exact to the cent, although the formulas are exact at every size.

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