Daily Compound Interest Calculator

This page applies FV = P × (1 + r/365)^(365 × t). The annual rate is divided into 365 daily slices, each slice is applied to the balance produced by the one before it, and the result is the largest ending value any realistic compounding frequency can give you at that rate. Every row in the table is computed from that closed form directly rather than accumulated day by day, so the yearly view, the monthly view, and the headline figure cannot drift apart through rounding.

The first thing worth noticing is in the monthly table. On 10,000 at 6%, the first month adds 50.12, the second adds 50.37, the third adds 50.62, and the twelfth adds 52.95. The step grows every single month, forever. That rising step is the entire mechanism, and it is the visible difference between this page and the simple interest calculator, where the step never changes at all.

The frequency ladder, and where it stops

A nominal 6% turns into a different effective annual rate depending only on how often it is applied. The ladder is short and it flattens fast:

• Once a year: 6.0000%
• Twice a year: 6.0900%
• Quarterly: 6.1364%
• Monthly: 6.1678%
• Weekly: 6.1800%
• Daily: 6.1831%
• Continuously, the mathematical ceiling: 6.1837%

Going from annual to monthly buys 0.1678 percentage points. Going from monthly all the way to daily buys 0.0153 more, and going from daily to compounding every instant of every day buys 0.0006 beyond that. The interesting part of the ladder is over almost as soon as it starts. If you have ever seen daily compounding described as a dramatically better deal than monthly, the ladder above is the counterargument, and it does not change shape at other rates.

Why the 365 is fixed, and why that turns out not to matter

This page uses 365 periods a year with no leap year handling, which sounds like an approximation worth worrying about. It is not. Run the same 6% over five years on 10,000 using 360, 365, and 366 periods and the answers are 13,498.25, 13,498.26, and 13,498.26. The effective annual rate reads 6.1831% in all three cases. Once you are compounding hundreds of times a year you have essentially reached the ceiling, so the exact count stops mattering. This is worth contrasting with simple interest, where the choice between a 360 and a 365 day divisor changes the answer by 1.39% of the interest.

One divisor question that does still matter

There is a version of the 360 question that is not harmless, and it appears on the lending side rather than the saving side. Some agreements define the daily rate as the annual rate divided by 360 and then charge it on all 365 days of the year. That is not a rounding convention, it is a rate increase. At a stated 6% it produces an effective 6.2716% rather than 6.1831%, and on 10,000 over five years it adds 56.35. The calculator models the honest version, so if your agreement uses a 360 day divisor with 365 day accrual, enter a slightly higher rate to reproduce it.

This is the question the page exists to answer, and the answer is smaller than the marketing around the phrase implies. Here is 10,000 at 6%, compounded daily against compounded annually, at six horizons.

• After 1 year: 10,618.31 against 10,600.00, a gain of 18.31
• After 5 years: 13,498.26 against 13,382.26, a gain of 116.00
• After 10 years: 18,220.29 against 17,908.48, a gain of 311.81
• After 20 years: 33,197.90 against 32,071.35, a gain of 1,126.54
• After 30 years: 60,487.53 against 57,434.91, a gain of 3,052.61
• After 40 years: 110,210.02 against 102,857.18, a gain of 7,352.84

Those are real gains and they grow: the daily account finishes 0.17% ahead of the annual one after a year and 7.15% ahead after forty. But compare against monthly compounding rather than annual, which is what most accounts actually offer, and the five year gain on 10,000 collapses from 116.00 to 9.75. Nine pounds, nine dollars, nine euros, over five years, on ten thousand. That is the true size of the daily advantage against a realistic alternative.

A better rate beats a better frequency, almost always

The cleanest way to see this is to price the frequency in rate terms. To match a 6% account compounding daily, a monthly account needs 6.0145% and an annual account needs 6.1831%. So the entire value of daily compounding, expressed as a rate, is about one and a half hundredths of a percentage point against a monthly competitor.

Put the other way round, if one account offers 4.50% compounded daily and another offers 4.75% compounded annually, the second is better. Over ten years on 10,000 the daily account reaches 15,682.69 and the annual account reaches 15,905.24, a difference of 222.56 in favour of the plainer product. A quarter of a percentage point on the rate outweighs the best compounding frequency available. Compare headline rates first, and treat frequency as a tiebreaker.

Fees are a much larger lever than frequency

Here is the comparison that puts the whole feature in proportion. Take 10,000 at 6% compounded daily over twenty years, which reaches 33,197.90. Now charge a 0.5% annual fee, so the account earns 5.5% instead. It reaches 30,039.17. That half a percent cost 3,158.72, which is 9.51% of the final balance.

Over the same twenty years, the entire advantage of daily compounding over annual compounding was 1,126.54. The fee is nearly three times larger than the benefit people go looking for. If you are optimising a savings decision and you have limited attention, spend it on the rate and the charges. Frequency is real, it is just last on the list.

How long the balance takes to double

At 365 periods a year, the doubling times are 69.32 years at 1%, 23.11 years at 3%, 13.86 years at 5%, 11.55 years at 6%, 8.67 years at 8%, and 6.93 years at 10%. The rule of 72 gives 72, 24, 14.4, 12, 9, and 7.2 for the same rates, so it runs slightly long at every one of them, and it is closest in the middle of the range where most people use it. Treat it as a mental estimate that is good to within a few percent, not as an answer.

This figure is derived from the effective annual rate shown beside it rather than from the nominal rate, which sounds like a technicality and is not. Solving the doubling time against the nominal rate on a page that compounds daily produces an answer about four months too long at every rate, and quietly disagrees with the effective rate printed directly above it.

On the saving side it is mostly a modelling choice

Plenty of savings accounts and money market accounts genuinely accrue interest daily and credit it monthly, and for those this page is the right model. But because the ladder flattens so quickly, daily accrual is rarely the reason to choose one account over another. It is more useful as an upper bound: whatever your account actually does, it cannot beat the number on this page at the same nominal rate, so if the daily figure still does not meet your goal, no change of frequency will get you there.

On the borrowing side it is doing real damage

This is where daily compounding stops being a rounding argument. Revolving credit is quoted as an annual rate and applied daily, and the numbers get uncomfortable quickly. Leave 5,000 on a card at 22.9% with no payments and after one year you owe 6,286.26, after two years 7,903.41, and after three years 9,936.58. The debt very nearly doubles in three years, and the precise doubling time is 3.03 years. The rate you are actually paying is 25.73%, not 22.9%, because the quoted figure is nominal.

The same arithmetic that makes daily compounding barely worth chasing on a 6% deposit makes it genuinely punishing on a 23% debt, because the gap between nominal and effective widens with the rate. At 6% the daily premium is 0.18 percentage points. At 22.9% it is 2.83.

The mistake that will silently inflate your result

Enter the nominal annual rate here, not the annual percentage yield. Savings products are frequently advertised by their yield, which already has the compounding folded in. A 6% nominal daily account has a yield of 6.1831%, and if you type 6.1831 into the rate field this page will compound it again and report an effective 6.3777%. Over ten years on 10,000 that overstates the balance by 336.63, which is larger than the entire benefit of daily compounding you were trying to measure. If your bank quotes a yield and you want to reproduce it, use the compounding frequency they state and the nominal rate underneath it.

What is not modelled

There are no deposits or withdrawals on this page, no rate changes partway through, no tax, and no fees. The controls for cashflows are switched off rather than hidden, with the reason shown on the control, because pretending they do not exist would be worse than saying where they live. If you need contributions, use the compound interest calculator, which handles deposits, withdrawals, annual increases, and any compounding frequency including 365. Fees can be approximated here by subtracting them from the rate you enter, since an expense ratio genuinely reduces what the balance earns.

Inflation, which is the number most people forget

Enter an inflation rate and the results add your balance restated in today's money. It matters more than compounding frequency by a wide margin. Ten thousand at 6% compounded daily reaches 33,197.90 after twenty years, but at 3% inflation that money buys what 18,380.87 buys today. The nominal figure more than tripled and the real one did not quite double.

The real return is computed as (1 + return) / (1 + inflation) minus 1 rather than by subtracting one from the other. At 6% against 3% inflation the exact answer is 2.9126%, not the 3.0000% the subtraction gives. The shortcut always overstates, and over twenty years the difference is visible in the final balance.

Which calculator to use instead

For anything with contributions or a different compounding frequency, use the compound interest calculator. For a fixed monthly investment, the SIP calculator is built for it. For drawing an income out of a balance, the SWP calculator reports when the money runs out. For growth measured per trade rather than per year, use the forex compound calculator, and for interest that never compounds at all, the simple interest calculator.