Compound Interest Calculator

What Is Compound Interest?

Compound interest is what happens when interest is left where it lands. Interest credited at the end of one period joins the principal, and the next period's interest is worked out on that larger figure. The rate never changes. The base it is applied to does, once every compounding period, for as long as the money stays put.

The Securities and Exchange Commission's investor glossary defines it in eight words: interest paid on principal and on accumulated interest. That sentence is the entire mechanism. Everything else on this page is arithmetic built on top of it.

The effect is small at first and then not small at all. $10,000 at 5% compounded annually earns $500 in its first year. In year 30 the same account earns $2,058.07 — not because the rate moved, but because the balance the rate is applied to had reached $41,161.36 by the time that year began, more than four times what was deposited.

Compound Interest vs Simple Interest

Simple interest is worked out on the original principal every period and on nothing else. $10,000 at 5% simple pays exactly $500 a year, year after year. Compound interest pays $500 in the first year and more in every year after it.

At five years the difference is $262.82, a rounding error against the deposit. At thirty it is $18,219.42 — more than the $10,000 that started the account. That is the shape of the whole subject: the compounding advantage is nearly invisible over a short horizon and decisive over a long one, which is why the length of the term is worth as much attention as the rate.

The compound column comes from this calculator with compounding set to Annually and the contribution field left empty. The simple column is plain multiplication done here, because the tool has no simple-interest mode — the Interest Type control does not switch the math.

Nominal Rate vs Annual Percentage Yield

The rate you type is the nominal annual rate: the headline figure, before compounding is taken into account. What you actually earn across a year is the annual percentage yield, and it is higher whenever interest is credited more than once a year. MathWorld uses the same vocabulary, calling the annual rate the nominal rate and the compounding periods conversion periods.

APY = 100 × [ (1 + Interest ÷ Principal) ^ (365 ÷ Days in term) − 1 ]

That is the formula in Appendix A to Part 1030 — Regulation DD, the rule behind every U.S. deposit account disclosure. Its own worked example: $61.68 of interest paid on $1,000 in a NOW account over 365 days is an APY of 6.17%. Enter $1,000 at 6% for 1 year with Monthly compounding here and the panel returns 1061.68 — the same $61.68, from the same arithmetic.

A 5% nominal rate is an APY of 5.0000% compounded annually, 5.0945% quarterly, 5.1162% monthly and 5.1267% daily. Compare accounts on APY, because it already contains the frequency. Type the nominal rate into this calculator, because the compounding menu applies the frequency for you.

How Do You Calculate Compound Interest?

Two formulas do the work: one grows a lump sum that is left alone, the other grows a stream of equal deposits. The calculator runs both and adds the results, which is why a worked example that quotes only the first will not reproduce the panel's answer once the contribution field is filled in.

The Compound Interest Formula

For a principal with no further deposits:

A = P × (1 + r/n) ^ (n × t)

• A — the ending balance, principal and interest together
• P — the principal, the amount in the account at the start
• r — the annual rate as a decimal, so 5% is 0.05
• n — compounding periods per year: 1 annually, 2 semi-annually, 4 quarterly, 12 monthly, 365 daily
• t — the term in years

Interest alone is A − P. There is no second formula for it and the panel does not print it, so subtract the principal you typed from the balance you got back.

The Formula When You Add Money Every Period

A regular deposit needs a second term — the future value of an ordinary annuity — because each deposit compounds for a different length of time. The one made in the first period has the whole term to grow; the one made in the final period earns nothing at all.

A = P × (1 + r/n) ^ (n × t)  +  PMT × [ ( (1 + r/n) ^ (n × t) − 1 ) ÷ (r/n) ]

PMT is the deposit credited at the end of each compounding period, and the calculator builds it from your two contribution fields: the Monthly Contribution Amount multiplied by 12 and divided by the Contribution Frequency. Enter 200 with Contribution Frequency on Quarterly and PMT becomes $600; put it on Yearly and PMT becomes $2,400.

That deposit is applied once per compounding period, not once a month, so the two frequency controls have to agree before the contribution figure means what you think it means.

Working It Out Step by Step

• Convert the rate. Divide the annual percentage by 100, so 5% becomes 0.05.
• Find the periodic rate. Divide by the compounding periods per year: 0.05 ÷ 4 = 0.0125 for quarterly.
• Count the periods. Multiply periods per year by years: 4 × 10 = 40.
• Grow the principal. Raise 1 plus the periodic rate to the number of periods, then multiply by the principal.
• Add the deposits, if there are any. Multiply the per-period deposit by ((1 + periodic rate) ^ periods − 1) ÷ periodic rate.
• Find the interest. Subtract the principal and every deposit from the ending balance.

Round once, at the moment you write the answer down. A periodic rate of 0.05 ÷ 12 truncated to four decimal places — 0.0042 instead of 0.00416667 — raises a ten-year balance on $10,000 from $16,470.09 to $16,535.83, an error of $65.74 introduced entirely by rounding early.

Compound Interest Example: $10,000 at 5% for 10 Years

Principal 10000, rate 5, duration 10, Compounding Frequency on Quarterly, contribution left empty.

A = 10,000 × (1 + 0.05 ÷ 4) ^ (4 × 10)

A = 10,000 × (1.0125) ^ 40

A = 10,000 × 1.6436195

A = 16,436.19

What the panel prints

16436.19

The readout shows 16436.19 — the raw number, no dollar sign, no thousands separator — and the breakdown area beneath it stays empty, because the formula returns one value and no detail segments. Interest earned is $6,436.19: the balance less the $10,000 you started with.

The Same Money With $200 a Month Added

Keep 10000, 5 and 10, move Compounding Frequency to Monthly, leave Contribution Frequency on Monthly, and enter 200 as the contribution.

• Periodic rate: 0.05 ÷ 12 = 0.00416667
• Periods: 12 × 10 = 120
• Principal grown: 10,000 × (1.00416667) ^ 120 = $16,470.09
• Deposits grown: 200 × [ ((1.00416667) ^ 120 − 1) ÷ 0.00416667 ] = $31,056.46
• Panel output: 47526.55

Of that balance, $34,000 is money you handed over — the opening $10,000 plus 120 deposits of $200 — and $13,526.55 is interest. Split the interest between its two sources and it is nearly even: the $10,000 lump earned $6,470.09, and the $24,000 of deposits earned $7,056.46. The deposits are 2.4 times the cash and produce only 9% more interest, because the average deposit has been invested for about five years rather than ten.

Compound Interest Chart: What $10,000 Grows To

Every figure in this table comes from this calculator with Compounding Frequency on Monthly and the contribution field left empty, so it isolates what compounding alone does to a lump sum.

Read down a column and you see what rate is worth; read across a row and you see what time is worth, and time wins. At 7%, the ten years between year 20 and year 30 add $40,777.59 to the balance — close to three times everything the account had grown to after five years.

Switch compounding to Annually and every figure drops a little: $16,288.95 instead of $16,470.09 at 5% over ten years, $76,122.55 instead of $81,164.97 at 7% over thirty. The ranking of the rows never changes.

How Long Does Money Take to Double?

Divide 72 by the annual rate for a quick estimate of the doubling time. It is a convention rather than a law, and it is at its sharpest near 8%.

The shortcut overshoots at low rates and undershoots at high ones, and the error stays under 3% across the whole range — at 2% it predicts 36 years against a true 35.00, at 10% it predicts 7.2 against 7.27. The exact answer is t = ln(2) ÷ ln(1 + r), with r as a decimal and interest compounded annually.

How Compounding Frequency Changes the Total

The Compounding Frequency menu offers five settings, the same five the SEC's own compound interest calculator carries: annually, semiannually, quarterly, monthly and daily. Here is what each is worth on $10,000 at 5% over ten years, with nothing else altered. The last column is worked out from the unrounded balances, which is why three of its four figures sit a cent above what subtracting the rounded column beside it would give.

Going from annual to quarterly is worth $147.25 over the decade. Going from monthly all the way to daily is worth $16.55. Frequency has a ceiling: compound the same money continuously, the mathematical limit as the periods grow without bound, and you reach $16,487.21 — fifty-six cents above the daily setting. Rate and term move the answer. Frequency mostly moves the marketing.

Match the setting to the account rather than to the largest number. U.S. savings accounts and CDs commonly credit interest daily or monthly; Treasury EE savings bonds are compounded semiannually, the Treasury applying the rate to a new principal every six months. An account's disclosure states its compounding period, and its APY already reflects it.

Frequency Counts for More as the Rate and the Term Rise

That verdict is tied to the run it came from. The annual-to-daily gap is interest earning interest inside the year, so it widens with the rate and with the term together. These runs use $10,000 with the contribution field empty and the term stretched to thirty years.

At 3% over thirty years the frequency setting is worth 1.33% of the ending balance. At 10% it is worth 15.06%, or $26,278.84. Nothing about the mechanism differs between those rows — the periodic rate is simply larger, so interest credited part-way through the year has more to earn on. Term does the same work: at 5%, the annual-to-daily gap is $12.67 over a single year and $1,592.86 over thirty.

What Regular Deposits Add

Set the principal to 0 and the calculator projects a savings habit on its own. This run uses 6%, both frequency controls on Monthly, and $250 a deposit.

The final column is the one worth watching. At five years the account is 86% your own money; at thirty it is 36% yours and 64% interest. On these settings the crossover — the first year in which accumulated interest exceeds everything deposited — lands in year 22, where $66,000 of deposits sit under $70,556.47 of interest.

Deposits and starting balance are not interchangeable levers. A dollar in the opening balance compounds for the full term; a dollar deposited in the final year compounds for eleven months at most, and the very last deposit earns nothing, because every deposit is credited at the end of its period rather than the start. That is why the same total, split differently between the two fields, returns different answers.

Doubling the Deposit Doubles the Balance

With the principal at 0 the ending balance is directly proportional to the deposit, because the deposit multiplies straight through the annuity term. Every row above can be rescaled: on the same 6% and Monthly settings, $500 a month over thirty years returns 502257.52, which is 251128.76 doubled to the cent, and $100 a month returns 100451.50, four tenths of it.

Put money in the principal box and the proportion breaks. With $10,000 there, 6% and thirty years, $250 a month returns 311354.51 and $500 a month returns 562483.27 — a rise of $251,128.76 rather than a doubling, because the lump-sum half of the formula never moved. Doubling a deposit doubles only the part of the balance the deposits built.

How to Read Your Result

One number comes back and nothing else. It fills the large readout as a plain figure to two decimals — 47526.55, not $47,526.55 — and the space below it stays blank, because this formula returns a single value with no breakdown rows attached.

Everything else is subtraction you do yourself. Money contributed is the principal plus the per-period deposit multiplied by the number of compounding periods; interest is the balance minus that. For 10000 at 5% over 10 years with Monthly compounding and 200 a month: $10,000 + (200 × 120) = $34,000 in, and $13,526.55 earned.

The page does not recalculate as you type. It opens with the panel empty, because the number fields start blank, and it stays that way until you press Calculate. Reset clears the panel back to its opening state.

Set Both Frequency Controls to the Same Cadence

A deposit is credited once per compounding period, and its size is the Monthly Contribution Amount scaled by 12 divided by the Contribution Frequency. Those two rules only agree when the compounding menu and the contribution control name the same cadence — and the form does not open that way. Compounding Frequency starts on Annually while Contribution Frequency starts on Monthly.

All six rows use $10,000 at 5% for 10 years with 200 in the contribution box. The first three deposit the same $24,000 and differ only in how often interest is credited — a spread of $1,050.66 across a decade. The last three are not the same savings plan at all: leave the menus as they open and a $200-a-month habit is booked as $200 a year, and pairing Daily compounding with Monthly contributions deposits $200 every single day.

If the cadence you want is missing from one of the lists, match the one that governs your deposits and accept a small error in the compounding. Being out by $1,050.66 of interest is a far smaller mistake than being out by $22,000 of deposits.

The Balance Is Before Inflation and Before Tax

The figure is nominal. It is what the statement will say at the end of the term, not what the money will buy by then, and not what is left after the interest has been taxed.

Both adjustments are one line of arithmetic on the balance. Real value is balance ÷ (1 + inflation) ^ years: $47,526.55 after ten years of 3% inflation is worth $35,364.22 in today's money. After-tax value is balance − (interest × tax rate): at 24% on $13,526.55 of interest, $44,280.18 survives. Interest inside a tax-sheltered account is not taxed as it accrues, so that second line does not apply to an IRA or a 401(k).

To price the same money against a longer run of inflation, use the Inflation Calculator.

Limits: When This Does Not Apply

The arithmetic here is exact. The assumptions fed into it are the part that can be wrong, and there are three places where the tool will not warn you that they are.

Four Fields Do Not Change the Answer

Interest Type, Expected Inflation Rate, Tax Rate on Interest Gains and Target Amount are rendered on the form but are not read by the calculation. The projection is always the compound future value: before inflation, before tax, and with no comparison against a goal.

That is testable in seconds. Enter 10000, 5, 10, Monthly compounding and 200 a month, then set Interest Type to Simple Interest, inflation to 3, tax to 24 and the target to 50000. The panel still returns 47526.55, identical to the run with those four left alone. The simple-interest comparison and the inflation and tax adjustments elsewhere on this page are arithmetic done here, not readouts from the tool.

One Fixed Rate Is a Scenario, Not a Forecast

The model applies a single rate to every period of the term. Savings rates are variable and move with policy; market returns arrive as a sequence of good and bad years, never as their average spread evenly. A thirty-year projection at one rate tells you what that assumption implies, which is genuinely useful, and nothing about what will happen, which is what people usually want from it.

Run it three ways — a cautious rate, a central one, an optimistic one — and treat the spread as the answer rather than any single number inside it. On $10,000 over twenty years with monthly compounding, 3% gives $18,207.55 and 7% gives $40,387.39; the honest answer is that range, not its midpoint. The tool also knows nothing about fees, which come out of the return before compounding starts, or about a deposit you skip.

Debt Compounds the Same Way

Nothing in the formula knows whether the balance belongs to you or to a lender. An unpaid credit-card balance compounds on exactly this arithmetic, usually daily, at whatever rate the statement prints. Enter the card's rate with Daily compounding and the projection shows what the debt becomes if nothing is ever repaid.

It will not model a payoff, though. A negative number in the contribution box is accepted and subtracted each period, but that is a level withdrawal, not an amortizing payment schedule, and a real card balance moves with every purchase.

For a card you are actually paying down, month by month, use the Credit Card Payoff Calculator.