ReckonBoxHow the compound interest calculator works
Compound interest is interest calculated on both the original balance and the interest already added to it. Type a starting balance, a rate, a term and a contribution, and this tool returns the ending balance, how much of it you put in, and how much the interest did.
It also prints every equation it runs, including the one for the tax.
The formula, with the letters defined
For a lump sum with no contributions:
A = P(1 + r/n)^nt
P is the starting balance, r the annual rate as a decimal, n the number of times interest compounds per year, and t the time in years.
Those two definitions earn their own sentence because the exponent swings on them. At 5% for 10 years compounded monthly, n times t raises the base to the power of 120. Read the letters the other way and you get 24, which is a different answer to a different question.
The contributions formula
FV = P(1 + r/n)^(nt) + PMT x [((1 + r/n)^(nt) - 1) / (r/n)]
The first term is the opening balance growing. The second is the future value of the contribution stream, where PMT is the amount you add each period. When contributions land at the start of each period, multiply that second term by (1 + r/n).
This used to be the thing worth pointing at, because the field ran the equation and hid it. That's changed. MoneyGeek now publishes the combined form outright, and CalculatorSoup surfaces the annuity component in its calculation steps. Two of the ten pages checked on 7 September 2026 show their working, so publishing the maths is no longer unusual enough to be a selling point.
The gap moved somewhere less obvious.
What compounding frequency is worth
Less than the marketing suggests, once you're past monthly.
| Compounding | Effective annual rate on a 5% nominal |
|---|---|
| Annually | 5.00% |
| Semiannually | 5.06% |
| Quarterly | 5.09% |
| Monthly | 5.12% |
| Daily | 5.13% |
The effective rate is (1 + r/n)^n - 1, which is what a savings APY expresses. Going from annual to monthly compounding buys you twelve basis points. Going from monthly all the way to daily buys one more. calculator.net makes the same point with a 6% example, and the shape of the curve is the useful part: the gains flatten hard, and a bank advertising daily compounding is advertising a rounding difference.
When the tax is charged, and why it moves the answer
$538.49, on identical inputs and an identical tax rate, decided purely by when the tax gets taken. That number is why this page exists in its current form.
We fetched ten competing calculators on 7 September 2026 to write this section. One of them, calculator.net's interest calculator, accepts a tax rate and reports an after-tax balance. None of the ten says how it applies the tax.
There are two defensible methods and they don't agree:
| Method | Ending balance |
|---|---|
| Gross, no tax | $47,526.55 |
| Tax on total interest, charged at the end | $44,144.91 |
| Tax on interest as it accrues | $43,606.43 |
Same $10,000 start, same $200 a month, same 5% compounded monthly over 10 years, same 25% rate. The spread exists because tax paid along the way never gets the chance to compound. Charge it annually and you're shrinking the base that next year's interest is calculated on, every year, for ten years.
This tool uses the first method: one flat rate against total interest at the end. That models a wrapper where the gain is taxed on realisation. The second models a taxable savings account where interest is reported and taxed each year as it's credited.
Neither is wrong. Picking one silently is what's wrong, so this page names the one it picked and hands you the gap.
A worked case
$10,000 starting, $200 a month, 5% a year compounded monthly, over 10 years.
| Component | Amount |
|---|---|
| Starting balance grown alone | $16,470.09 |
| Contributions grown | $31,056.46 |
| Ending balance | $47,526.55 |
| Total you put in | $34,000.00 |
| Interest earned | $13,526.55 |
Two thirds of the ending balance traces to the contributions, with the opening deposit supplying the rest. A headline "power of compounding" chart tends to blur that split, so the tool prints the share.
Shift the contributions to the start of each period and the second term gains a factor of 1.00417, worth one month of growth. Tiny on any single payment. It accumulates.
What this calculator doesn't do
The rate is an assumption you typed, and nothing here turns it into a forecast. A savings APY moves during any period long enough to be worth modelling, and an investment return isn't fixed at all. A variable-rate path would be invented, so the rate holds flat and this sentence is the disclosure.
Jurisdiction-specific tax treatment belongs with an accountant. The tool applies one flat rate to interest and shows you the alternative timing above; it doesn't know about your allowances, brackets, or wrappers.
Day-count conventions are absent on purpose. They're grounded in lending, the simple interest calculator carries them, and importing a lending convention into a savings projection would put them where no source does.
Results are arithmetic on your inputs and aren't financial advice. For decisions about your money, speak to a licensed financial adviser. To run the relationship backwards, the present value calculator discounts a future sum to today, and the interest rate calculator solves for a rate you weren't told.
Frequently asked questions
What is the compound interest formula? For a lump sum it is A = P(1 + r/n)^nt, where P is the starting balance, r the annual rate as a decimal, n the number of times interest compounds per year, and t the time in years. The exponent is n times t, so 10 years compounded monthly raises the base to the power of 120.
What is the formula when you add regular contributions? FV = P(1 + r/n)^(nt) + PMT x [((1 + r/n)^(nt) - 1) / (r/n)], where PMT is the regular contribution. Multiply the contributions term by (1 + r/n) when payments land at the start of each period. MoneyGeek publishes the same combined equation and CalculatorSoup shows the annuity component in its steps, so the maths is checkable in more than one place.
Does it matter when tax is charged on the interest? It's worth $538.49 on this tool's default scenario. Charging 25% against total interest at the end leaves $44,144.91, while charging it on interest as it accrues leaves $43,606.43, because tax paid along the way never compounds. This tool uses the first method. Of ten calculators fetched on 7 September 2026, only one accepts a tax rate at all and none states which method it uses.
How much difference does compounding frequency make? Less than most people expect once you pass monthly. A 5% nominal rate is worth 5.00% effective compounded annually, 5.12% monthly and 5.13% daily. The step from annual to monthly is twelve basis points and the step from monthly to daily is one.
What is the difference between the interest rate and APY? The interest rate is the nominal annual figure, and APY is what it's worth after a year of compounding: (1 + r/n)^n - 1. A calculator asking for both an APY and a compounding frequency is asking for overlapping information. This tool takes the nominal rate and reports the effective rate your chosen frequency produces, so compounding gets applied in exactly one place.
Does the contribution timing really matter? It's worth exactly one compounding period of growth. Paying at the start of each period multiplies the contributions term by (1 + r/n), which on a monthly schedule at 5% is a factor of 1.00417. Small per period, and it compounds over a long horizon.
Is this the same as a savings calculator or a future value calculator? Mathematically yes, which is why one page covers all three. A savings calculator is a starting balance plus contributions at a rate, and future value with a payment is the same annuity equation. Several of the calculators checked for this page ship the two as separate tools without explaining anywhere how they differ.
How should the rate be treated? As an assumption you typed. A real savings APY changes during the period being modelled and an investment return isn't fixed, so the output is arithmetic on the number you supplied. For decisions about your money, speak to a licensed financial adviser.
Sources
Fetched 7 September 2026.
- MoneyGeek compound interest calculator, which publishes the combined contributions equation
- CalculatorSoup compound interest calculator, showing the annuity component in its calculation steps
- calculator.net interest calculator, the one fetched page with a tax rate input
- calculator.net compound interest calculator, for the effective-rate example and continuous compounding
- TheCalculatorSite compound interest calculator, for the standard definitions of n and t
- Financial Mentor compound interest calculator, which adjusts for inflation
- Western and Southern compound interest calculator, which labels its return before tax