Compound Interest Calculator

Compound interest in one paragraph

You earn interest on your principal, then the next period you earn interest on both the principal and the interest from the period before. The maths is simple; what catches people out is the curve. For the first few years nothing dramatic happens; then the curve pulls away from the straight line a linear mental model would sketch. There is no single bend point: at 7% the balance doubles roughly every ten years, so each decade adds more than the one before, and the longer the horizon the steeper the late years look.

The formula in plain English

The formula panel below the calculator shows the general form: the principal grows by P(1 + j)^nt where j is the rate per compounding period (the rate as entered, divided by 100 and by the number of periods a year), and every contribution is compounded individually from the period it lands in (the summation term), because contributions can escalate each year and no single level-annuity multiplier covers that. Strip the notation and you're saying: take the rate per compounding period, add 1, raise it to the power of how many periods remain, and do that for the starting amount and for each deposit from its own start date. When the annual increase is set to zero, the summation collapses to the familiar level-annuity form PMT × [((1 + j)^nt − 1) / j], the simplified case. Monthly compounding at 7% annually isn't 7% per month: it's 0.5833% per month, applied 120 times over 10 years. That repetition is where the acceleration comes from.

How to use the calculator step by step

Enter your initial amount, the annual interest rate, and how long you plan to leave the money invested. Pick a compounding frequency (annually through to daily, or Custom with your own periods-per-year figure) to match how your account or investment actually credits interest. If the rate is quoted per month or per day rather than per year, the Rate Quoted Per selector next to the rate field takes it as written. If you make regular deposits, enter the contribution amount and how often. Add an annual increase percentage to step contributions up over time, which is the structure some pension and salary-linked savings plans use. The result, the breakdown table and the comparison chart all recompute as you type. The currency selector at the top of the input panel renders every figure on the page in the chosen unit.

What each result means

The headline figure is the future value: principal plus all contributions plus all compounded interest. Below it the calculator surfaces total interest earned (the part that came from the money working rather than from your deposits), total deposited (principal plus the sum of every contribution), and the effective annual yield: the true once-a-year-equivalent rate after compounding. The Time-to-Double figure uses the closed-form result t = ln(2) / (n × ln(1 + j)), which is the precise version of the Rule of 72 mental shortcut. When contributions are present the calculator also reports a Money-on-Money Return: the cumulative ratio of interest earned to total deposited, which describes how much extra came back on every unit you put in.

After tax and inflation, what you keep in real terms

Many compound calculators stop at the gross future value. The gross figure is the number on a statement; the net real value is the number that translates into purchasing power. The Tax Rate input applies to the interest portion of each compounding period, not as a one-off tax at the end, which mirrors how a taxable brokerage or savings account behaves outside of a tax-advantaged retirement account. The drag compounds in reverse: a 25% tax on returns does not reduce the final balance by 25%, it reduces it by considerably more over a long horizon because every year's interest is taxed before it can compound. At 7% nominal over 30 years, a 25% tax shrinks the final figure by roughly 40% rather than 25% (verifiable by setting principal=10,000, rate=7%, years=30, tax_rate=25%, contribution=0 in the calculator and comparing the After-Tax Future Value row to the Future Value row). Layer the inflation input on top to convert that net figure into today's purchasing power, and the resulting Real After-Tax Value row reflects what the projection is worth in goods and services for any goal denominated in real-world spending.

Scenarios that show the curve

Starting from 1,000 of any currency at 7% with monthly compounding, ten years lands at about 2,010, roughly double. Twenty years reaches about 4,038; thirty years about 8,116. Each additional decade multiplies what is already there rather than adding a fixed amount. Now turn on a 200/month contribution at the same rate over 30 years and the figure rises to about 252,000; in that scenario, annual interest first exceeds the year’s contributions around year 11. Add a 3% annual contribution increase and the projection rises to about 342,000. Apply a 25% tax rate on returns and the same scenario lands at about 251,600 instead of 342,000: about 26% lower because the tax compounds in reverse against every year of interest.

How starting early compares with starting big

At 7%, the start-early-versus-save-more comparison produces its often-quoted result, and it does hold: a 25-year-old contributing 100 a month for ten years and then stopping (12,000 in total) finishes ahead at 65 of a 35-year-old contributing 100 a month for thirty years and putting in 36,000. The early money gets forty years of compounding against thirty. The outcome is rate-sensitive: below roughly 6.1% the arithmetic flips and the larger contribution stream wins. Running both scenarios side by side here turns a saying into a number that can be checked.

The fee, inflation and tax trio

Nominal compound growth describes the gross outcome only. The figure that gets kept after costs is smaller, for three reasons.

Fees. A 1% annual fee on an investment returning 7% doesn't cost 1%: over a 20-year horizon it reduces the final balance by about 18%, and over 30 years by about 26% (verifiable by running the same scenario once at rate=7% and once at rate=6% with the default monthly compounding; on annual compounding the same comparison gives about 17% and 25%). The fee compounds too, in the wrong direction, and fund-level, platform and advice fees stack.

Inflation. The 8,116 from the 30-year example above is in today's money only if inflation is zero. At 2.5% average inflation, the real purchasing power is closer to 3,870. The figure on a future statement is the same; the spending power it represents is not. The inflation input surfaces both numbers.

Tax. The Tax Rate input handles this directly. Outside of tax-advantaged accounts and pensions, tax is paid on interest or gains along the way. The calculator applies the tax rate to the interest portion of every compounding period, so the after-tax balance compounds going forward, matching how the drag works in a taxable account rather than as a single end-of-period deduction.

Does compounding frequency matter?

The lift from compounding more often is smaller than the frequency alone suggests. Going from annual to monthly compounding at 7% over 30 years moves 1,000 from about 7,612 to about 8,117, a 6.6% lift on the final figure. Moving from monthly to daily adds about another 48 (a further 0.6% lift). Whether compounding happens matters enormously; how often matters at the margins. Compounding frequency moves the effective annual yield by roughly 5 basis points at 3% and 13 at 5%, rising to about 52 at 10%. At typical savings rates a small gap in the quoted annual rate outweighs the frequency; at high rates the frequency can close a wider gap. The effective annual yield row settles the comparison in either direction.

What the comparison chart shows

The chart plots multiple lines side by side: compound balance (the money working at the rate entered), after-tax balance (when a tax rate above zero is set), simple interest (the principal earning the same rate with nothing reinvested, and contributions added at face value), and no-interest principal (just the deposits). The gap between the compound and simple lines is what compounding contributes: for the first few years the gap is invisible, then it widens. The gap between the gross compound line and the after-tax line is the tax drag, which also widens with time. Looking at all the lines together makes it concrete how much of long-term growth is the rate, how much is the compounding effect, and how much is taxed away.

Reading the year-by-year breakdown table

Below the chart, every period of the projection is laid out in a sortable table. The columns are compound balance, after-tax balance (when a tax rate is set), the simple-interest and no-interest comparison lines, real inflation-adjusted balance (when an inflation rate is set), interest for that period, accrued interest to date, and contributions for that period. Switch the breakdown to monthly to see month-by-month figures (capped at 360 rows for readable scrolling). Click any column header to sort. The period where annual interest first exceeds the annual contribution is the tipping point where invested money does more work than fresh deposits. In the 200-a-month at 7% scenario above, annual interest first exceeds the year’s contributions around year 11; the exact year depends on the contribution, escalation and rate mix.

Adding withdrawals to the projection

Set a withdrawal amount and frequency and the same simulation runs the drawdown side of the picture. Withdrawals are taken after interest is credited for the period, so the balance that compounds into the next period is the post-withdrawal figure. The withdrawal can escalate each year by a percentage, which mirrors how a drawdown plan indexed to inflation behaves over a long retirement. Deposits and withdrawals can run together: money in monthly, money out quarterly is a single scenario here, not two. If the withdrawals outpace the growth, the balance floors at zero rather than going negative, and a Total Withdrawn row is joined by a Balance Reached Zero After row showing the point at which the pot could no longer cover a full withdrawal. Starting from 100,000 at 5% with monthly compounding and 500 a month withdrawn, twenty years ends at about 65,750 after 120,000 has been taken out; the balance falls but the pot outlives the withdrawals. Drop the rate to 3% on a 50,000 pot and the same 500 a month empties it in about 9 years 8 months. Withdrawals reduce the balance but are not netted off the interest tally, so Interest Earned stays the sum of interest credited across the term. In the 50,000 example above, about 57,600 is paid out while about 7,600 of that is credited interest; the rest is the original capital coming back.

Rates quoted per month, week or day

Rates are not always quoted annually. A savings product might advertise a monthly rate and a short-term facility a daily one. The Rate Quoted Per selector scales whatever is typed into the nominal annual rate the rest of the maths runs on: 0.5% entered as a monthly rate is a 6% nominal annual rate, which at monthly compounding produces the same projection as typing 6% with the selector left on Annual. Both routes land on 18,193.97 from a 10,000 start over ten years. Keeping the two settings separate matters because how a rate is written down and how often interest is credited are different questions.

A compounding frequency the dropdown does not list

Set Compounding Frequency to Custom and the Compounds Per Year field beside it takes over, which covers the counts the dropdown does not name: a 13-period four-weekly cycle, 18 periods, or anything else a product actually uses. The named options are shortcuts for the common cases; the custom field accepts any figure from 1 to 365. At 5% over ten years on 10,000, semi-monthly compounding (24 periods) lands at about 16,479 against 16,470 for monthly, a reminder that period count moves the result at the margins once the rate and the term are fixed.

Things to watch for

One trap is entering nominal historical returns as a forward expectation. Long-run world equity returns have been reported at around 5% annualised in real terms over 1900–2024 (UBS Global Investment Returns Yearbook, formerly published by Credit Suisse, building on Dimson, Marsh & Staunton’s Triumph of the Optimists), with US markets higher, and any individual 10-year window can deliver well above or well below that. A flat 200/month contribution is another quiet distortion: it feels right for the next year but not for year 30, when both salaries and prices have roughly doubled, which is what the annual increase input corrects. Tax is a third: projections that exclude it sit above what a taxable account actually delivers. Sequence of returns is the subtlest. The output assumes smooth growth, and for a pure lump sum the order of good and bad years genuinely does not change the end figure, but with regular contributions it does, because an early drawdown means later deposits buy in at lower levels, so the same average return can land at a materially different end value depending on when the volatility arrives.

Compound interest accrues to debt-holders too

The same mechanic that grows a savings account is what makes a credit card balance at 22% APR difficult to clear. 3,000 at 22% compounding monthly doubles roughly every 3.2 years if no payments are made: the same maths, pointed the other way. The debt tools in this library use the same formula; running a savings scenario next to a debt scenario is often a clarifying comparison. For someone with 20,000 in a tax-advantaged account compounding at 5% and 8,000 on a credit card compounding at 22%, the credit card balance compounds faster than the savings, so net worth shrinks even when the savings figure on paper grows.

What the calculator can't model

Every projection tool simplifies. This one assumes a constant rate, a fixed compounding frequency, a flat tax rate (real systems have brackets, allowances, and variable rates), and an inflation figure entered manually. Regular withdrawals are modelled, but only as a scheduled amount that escalates at a set percentage, not the irregular, event-driven withdrawals real life produces. Real investment journeys also include changing rates, market volatility, varying tax situations, and behavioural responses to drawdowns. The output is best read as the cleanest possible version of one scenario rather than a forecast. A projection like this is typically used for recalibrating intuition about how long horizons compound, not for predicting the future.