Compound Interest Calculator

Every figure on this page comes out of one relation: FV = P × (1 + r/n)^(n × t). P is the money you start with, r is the annual rate written as a decimal, n is the number of times interest is applied each year, and t is the number of years. The exponent is where the interesting behaviour lives. Interest is not added to your principal, it is added to your balance, and next period that larger balance earns interest of its own. That is the whole idea, and everything else on this page is a consequence of it.

Why the table can show months even when interest compounds quarterly

Choosing quarterly compounding and then asking for a month by month table looks like a contradiction, since nothing happens to the balance in two months out of every three. Rather than showing you two flat rows followed by a jump, the schedule spreads each compounding period across the months inside it by growing the balance at (1 + r/n)^(n/12) every month. That factor is built so that twelve of them multiply out to exactly one year of growth at your chosen frequency, which means the monthly table and the annual formula land on the same number rather than drifting apart by rounding. On a balance of 10,000 at 6% compounded quarterly for ten years, the simulated monthly path and the direct formula agree to within a ten billionth of a cent.

What accrued interest counts, and what it does not

The accrued interest column is not simply your balance minus what you started with. It subtracts every deposit you made and adds back every withdrawal you took, so it isolates the growth the account produced from the capital you supplied. This matters most when you are contributing monthly, because a balance that has climbed to 200,000 tells you very little on its own. Knowing that 96,000 of it is money you put in and 104,000 is interest tells you whether the compounding is doing real work yet.

Deposits at the start of a period against deposits at the end

The timing control moves your contribution to either side of the interest calculation. Deposit at the beginning and every payment sits in the account for one extra compounding period before you stop; deposit at the end and it does not. The effect is small per payment and larger than you might guess in aggregate. Paying 500 a month for twenty years at 8% with monthly compounding finishes at 296,473.61 if the deposits land at the start of each month and 294,510.21 if they land at the end, a gap of 1,963.40. There is a neat check hiding in those two numbers: divide one by the other and you get 1.00666667, which is precisely one month of growth at 8% a year. That is not a coincidence, it is the definition of the difference.

In practice, pick the setting that matches reality rather than the one that produces the nicer number. Salary deductions and standing orders usually go in near the start of the month. Money you sweep out of a current account once you see what is left usually goes in near the end.

Withdrawals stop when the money runs out

If you model withdrawals larger than the account can sustain, the balance stops at zero instead of going negative, and each month only takes out what is actually there. This is deliberate, because a negative balance would quietly turn into a compounding debt and produce a projection that means nothing. It also changes how you should read the total withdrawn figure. Taking 500 a month from 10,000 at 4% empties the account after roughly 21 months, so a ten year plan reports about 10,366 withdrawn in total rather than the 60,000 you asked for. When the total withdrawn comes back smaller than your schedule implies, that is the calculator telling you the plan does not survive the horizon.

Contributions that rise each year

Real contributions rarely stay flat for decades, so deposits can carry an annual increase. Setting one reveals something worth understanding before you rely on it. Paying 500 a month for 25 years at 8% ends at 475,513 on 150,000 of contributions. Adding a 5% annual increase raises the contributions to 286,363, which is 91% more money, and the ending balance to 745,841, which is only 57% more. The uplift is real and worth having, but it is smaller than the extra money you put in, because a raise applied in year 20 buys you five years of compounding rather than twenty five. Every year you delay increasing a contribution costs you less than most people fear. Every year you delay starting one costs you more.

The rate you are quoted is not always the rate you earn

A nominal annual rate is a headline figure that ignores how often interest is applied. The effective annual rate folds the compounding back in and tells you what you actually earn across a year. At a nominal 6%, the effective rate depends entirely on frequency:

• Compounded once a year, the effective rate is 6.0000%
• Twice a year, 6.0900%
• Quarterly, 6.1364%
• Monthly, 6.1678%
• Daily, 6.1831%

This is the difference banks are pointing at when they quote APR on what you borrow and APY on what you save. The two describe the same underlying arithmetic viewed from opposite sides of a balance sheet. If you are comparing two products, compare effective rates or compare nominal rates at the same frequency. Comparing one of each will mislead you every time.

Compounding frequency matters far less than almost everyone expects

Daily compounding gets marketed as though it were a different asset class. Run the numbers and the effect is modest. Ten thousand at 6% for ten years grows to 17,908.48 compounded annually and 18,220.29 compounded daily. The entire benefit of moving from one compounding period a year to 365 is 311.81, which is 1.74% of the result. Now change the rate instead: the same ten thousand at 7%, compounded only once a year, reaches 19,671.51. One extra percentage point of return beats the whole annual to daily upgrade by 1,451.22, roughly four and a half times over.

The practical reading is that frequency is a tiebreaker, not a strategy. If two accounts pay the same rate, take the one that compounds more often. If one pays meaningfully more, take the rate and stop thinking about the frequency. And be suspicious of any product that leads with how often it compounds rather than what it pays.

Time does more work than the amount you contribute

Compare two savers, both earning 8% with monthly compounding. The first pays in 300 a month for forty years and contributes 144,000 in total. The second pays in 600 a month for thirty years and contributes 216,000. The first finishes with 1,047,302 and the second with 894,216. Starting ten years earlier wins by 153,087 while putting in 72,000 less. You can reproduce both runs above by changing only the monthly deposit and the number of years. If you are choosing between waiting until you can afford a serious contribution and starting now with a small one, the arithmetic is not close.

When interest starts outpacing your own deposits

There is a moment in every contribution plan when the account earns more than you have ever paid into it. Starting with 10,000 and adding 500 a month at 8%, that crossover arrives at month 173, a little over fourteen years in, with the balance at 193,314 split between 96,500 of contributions and 96,814 of interest. Watch the interest share climb from there:

• After ten years, the balance is 113,669 and 38.4% of it is interest
• After twenty years, 343,778 and 62.2% interest
• After thirty years, 854,537 and 77.8% interest
• After forty years, 1,988,238 and 87.4% interest

The first decade feels like saving because it mostly is. The fourth decade is where the account is doing something you could not have done by putting money aside. This is also why abandoning a plan at year eight, when it still looks like a savings account, forfeits the part that made it worth starting.

The rule of 72, and where it quietly goes wrong

Divide 72 by your rate and you get a rough number of years to double your money. It is a useful piece of mental arithmetic and it is at its best around 8%, where it says 9.00 years against a true 9.01. Away from that point it drifts in a predictable direction. Below 8% it is pessimistic: at 2% it claims 36 years when the real answer is 35. Above 8% it turns optimistic: at 12% it claims 6.00 years against a true 6.12, and at 20% it claims 3.60 against a true 3.80. The results panel on this page reports the exact figure, ln(2) divided by ln(1 + r), so you can use the rule for a quick sanity check and the calculator for anything you plan to act on.

What your balance will actually buy

Enter an inflation rate and two more results appear: your balance restated in today's money, and your real return after inflation. Both use division rather than subtraction, because prices and returns are ratios rather than quantities. The real rate is (1 + return) divided by (1 + inflation), minus one. At 10% returns and 6% inflation that gives 3.77%, not the 4% you get from subtracting, and the gap grows with the horizon. Ten thousand compounding at 10% for thirty years reaches 174,494, which is worth 30,381 in today's prices at 6% inflation. Using the subtraction shortcut instead would have told you 32,434, overstating your real position by 6.8%.

There is a satisfying consistency check built into those two figures. Growing your starting balance at the real rate for thirty years, and discounting the nominal balance back by thirty years of inflation, give the same 30,381. That identity is covered by the test suite, so the two results on the page cannot silently disagree.

A projection is only trustworthy if you know where it stops describing the world. Four assumptions are baked into every number above, and each one is a place where reality can diverge from the chart.

A constant rate is a convenience, not a forecast

Markets do not return 8% every year, they average something like it while lurching around. For a single lump sum that distinction genuinely does not matter: gains of 30%, then a loss of 10%, then a gain of 20% leave you at 140,400 on a starting 100,000 no matter which order they arrive in, because multiplication does not care about sequence. Add contributions and the order starts to matter a great deal. Paying in 12,000 a year across those same three returns produces 44,208 in one order and 46,488 in the other, a difference of 2,280 from an identical average, purely because of how much money was exposed to each year.

This is also why averaging percentage returns overstates what you kept. A 50% gain followed by a 50% loss reads as an average of zero and leaves 75,000 of every 100,000. Volatility takes a real bite that a single steady rate cannot show, so treat a constant rate projection as the centre of a range rather than the line your account will follow.

Fees compound in exactly the same way your returns do

An annual charge is not a small subtraction from your final balance, it is a permanent reduction in the rate that gets raised to a power. One hundred thousand growing at 8% for thirty years reaches 1,006,266. The same money at 7%, which is what a one percent annual charge leaves you, reaches 761,226. That single percentage point costs 245,040, or 24.4% of the outcome. Even a half percent charge costs 130,770, which is 13.0%. Model this by entering the rate you expect after charges rather than the headline rate, since a fee genuinely reduces what the account earns.

Tax is not modelled

Results here are before tax. If the account is sheltered, that is the right basis. If it is taxable, how much it costs you depends on your jurisdiction, whether growth is taxed annually or only when you sell, and your own marginal rate, none of which a general calculator can know. The usable approximation is to enter a rate reduced by the tax you expect to pay on the growth, and to remember that annually taxed accounts lose more than the headline rate suggests, because tax paid this year is also money that stops compounding.

Deposits are assumed to arrive

The schedule assumes every contribution is made on time for the full term. Careers, illness and moving house all interrupt that. If you want a more defensible number, run the plan once as intended and once with a couple of years of contributions removed, and treat the lower figure as your floor.

This page is the general purpose model: a starting balance, an optional stream of deposits or withdrawals, and any compounding frequency. Several situations are better served by a page built around them.

• Investing a fixed amount every month with no starting balance is what the SIP calculator is shaped for, including annual increases to the contribution.
• Drawing a regular income from a pot you have already built is the SWP calculator, which reports how long the money lasts rather than what it grows to.
• Products that credit interest every day are covered by the daily compound calculator, which fixes the frequency at 365 and focuses on the effective rate.
• Interest paid only on the original principal, with no compounding at all, belongs on the simple interest calculator. Comparing the two side by side is the clearest way to see what compounding is worth.
• Modelling a trading account that grows by a percentage each period is the forex compound calculator.

Whichever you use, the calculation runs entirely in your browser. Nothing you type is sent anywhere, which is why there is no account to create and no results to save on our side. Export the breakdown if you want to keep it.