Compound Interest Calculator

What compound interest does to a regular contribution

Two different things are growing at once here, and keeping them apart is most of the understanding. The starting amount sits there and multiplies: after t years at a rate i per compounding period, applied m times a year, it is worth P · (1 + i)^(m·t). The regular contribution is a stream of payments, each of which has less time left to grow than the one before it, so its value is the sum of a shrinking set of powers — which collapses to the annuity formula C · ((1 + j)^n − 1) / j, where j is the rate earned over one contribution period and n is how many contributions you make. The page adds the two and reports the total, what you paid in, and the difference.

A worked example, all the way through

Take the numbers the page loads with: 5,000.00 to start, 250.00 added at the end of every month, a nominal 6% a year compounded monthly, over 30 years. The rate per month is 0.06 / 12 = 0.005, and there are 360 contributions. The lump sum becomes 5000 × 1.005³⁶⁰ = 30,112.88. The contributions become 250 × ((1.005³⁶⁰ − 1) / 0.005) = 251,128.76. Together: 281,241.64, against 95,000.00 actually paid in — so 186,241.64, about 66% of the final balance, is interest.

The year-by-year table is where the shape becomes obvious. Its Put in so far and Interest so far columns are running totals, and the CSV export adds the per-year figures beside them. The contribution never changes — it is 3,000.00 every single year — but the interest earned during year 1 is 392.28 and the interest earned during year 30 is 16,243.37, forty-one times as much, on exactly the same annual saving. That is the entire mechanism: the interest from earlier years is itself earning. Stop the same plan at 10 years and it holds 50,066.82 (of which 35,000.00 is yours); at 20 years, 132,061.25 against 65,000.00. The money you put in grows linearly; the balance does not.

Nominal, effective, and why the compounding box matters

A quoted rate is almost always nominal: an annual headline that gets divided by the number of compounding periods and applied that many times. That is not the same as what you actually earn in a year. The effective annual rate is (1 + R/m)^m − 1, and the page prints it beside the nominal rate you typed so the two are never confused.

The gaps look small and are not. On the worked example above, switching the compounding box from monthly to yearly and changing nothing else takes the 30-year balance from 281,241.64 down to 272,345.70 — 8,895.94 of difference from one dropdown. The increments also shrink fast: going from yearly to monthly buys 0.168 percentage points, while going from monthly all the way to daily buys only 0.015 more, and the theoretical limit of infinite compounding (e^0.06 − 1) is 6.1837%. Anyone advertising "compounded continuously" as a headline feature is advertising the last 0.0006 points.

When the contribution frequency is not the compounding frequency

Most real plans mismatch these — money goes in monthly while interest is credited quarterly, or money goes in weekly while interest is credited daily. Rather than fudge it, this tool derives the rate for one contribution period from the compounding rate: j = (1 + i)^(m/k) − 1, where m is compoundings per year and k is contributions per year. With quarterly contributions against monthly compounding, m/k = 3, so each payment earns three months of growth before the next arrives. With yearly contributions against quarterly compounding, m/k = 4. The identity that keeps it consistent is (1 + j)^n = (1 + i)^(m·t): the contributions and the lump sum grow at exactly the same underlying rate, so the two halves of the answer can be added without any correction.

End of the period or the start of it

By default every contribution lands at the end of its period — the ordinary annuity that finance textbooks use, and the conservative reading, since the final payment earns nothing at all. Paying at the start instead gives every payment one extra period of growth, which multiplies the whole annuity by (1 + j). It is a bigger effect than it sounds over a long term: 2,000.00 a year at 6% compounded yearly for 40 years is 309,523.93 paid at year end and 328,095.37 paid at year start — 18,571.44 apart, for the same 80,000.00 of contributions, purely from timing.

Zero percent is arithmetic, not an error

At a 0% rate the annuity formula divides by zero, so the calculator does not use it: the balance is simply the starting amount plus the contribution times the number of payments. 10,000.00 plus 100.00 a month for 10 years is exactly 22,000.00, and the interest line reads 0.00. It is a useful baseline — running your plan at 0% shows you exactly how much of the projected balance is the arithmetic of saving rather than the arithmetic of interest.

How the numbers are computed, and how far to trust them

Every balance comes from the closed form evaluated once, and every row of the year table is an independent evaluation at t = 1, 2, 3 … rather than a running total stepped forward — so row 30 carries no accumulated rounding from row 1, and the last row always equals the headline figure exactly. Money is reported as whole cents, with a single rounding at the display boundary. The maths lives in a separate module pinned by 24 golden vectors asserted to the cent, each one cross-checked against an independent term-by-term summation of the contribution stream rather than against the formula itself.

Two approximations are baked into the frequency options, and they are worth knowing before trusting the last digits. Weekly means 52 equal periods a year and every two weeks means 26; a calendar year is about 52.18 weeks, so a real weekly plan slips in an extra payment roughly every six years and this model does not. Daily compounding means 365 periods a year, with no leap-day adjustment. Both are the conventions most published calculators use, and both are slightly conservative.

What this deliberately does not do

Inflation, tax, fees and variable returns are not modelled at all. A balance of 281,241.64 thirty years from now is 281,241.64 of future money; at 2.5% average inflation it would buy roughly what 134,000 buys today, and this page does not compute that for you. Interest is frequently taxable, platform and fund fees come off the return before it compounds, and no real investment delivers the same rate every year for thirty years — a constant rate is a modelling convenience, not a property of the world. This page also offers no advice, no product, no provider and no recommendation: it is a calculator for an arithmetic question, it has no opinion about what you do, and none of its output is a forecast. Nothing you type is uploaded, no rate is fetched, and no currency is converted — the currency box changes the symbol and the digit grouping only.

If the question is the other direction — what a debt costs while interest compounds against you — the Loan Calculator builds an amortization schedule in exact cents and shows what an extra payment saves.

Questions people ask

What does this calculator actually compute?

It computes the closed-form future value of two things added together: a starting amount left to grow, and a regular contribution paid every period. With 5,000.00 to start, 250.00 added every month, a nominal 6% a year compounded monthly and a term of 30 years, the balance ends at 281,241.64 — of which 95,000.00 is money you put in and 186,241.64 is interest. You can run any one of the three shapes: a lump sum alone, a regular contribution alone, or both together.

Is the rate I type nominal or effective?

Nominal. The rate box takes the quoted annual rate, and the compounding box says how many times a year that rate is applied. Those two together produce the effective annual rate, which the page shows beside the nominal one: a nominal 6% compounded monthly is an effective 6.1678% a year, and a nominal 12% compounded monthly is an effective 12.682503%. Set compounding to yearly and the two numbers are identical.

Does this account for inflation, tax or fees?

No. Inflation, tax, fees and variable returns are not modelled at all. The figure is compound interest at one constant rate and nothing else, so a balance of 281,241.64 thirty years out is 281,241.64 of future money, not of today's money. Anything that takes a slice — a platform fee, tax on the interest, a fund's expense ratio — lowers the rate that actually applies, and any year whose real return differs from the rate you typed moves the answer.

Why does monthly compounding beat yearly compounding at the same rate?

Because interest credited sooner starts earning interest itself. 1,000.00 at a nominal 12% compounded once a year is 1,120.00 after a year; the same 1,000.00 at a nominal 12% compounded monthly is 1,126.83, because each month's 1% joins the balance that the next month's 1% is charged on. That is a gap of 6.83 on a thousand in a single year, and it widens with the term.

What if my contribution frequency is not the compounding frequency?

That case is handled directly rather than approximated. The rate earned over one contribution period is derived from the compounding rate as (1 + i) to the power m/k, minus 1 — where i is the rate per compounding period, m is the number of compounding periods a year and k is the number of contributions a year. Quarterly contributions against monthly compounding therefore earn three months of growth between payments, and yearly contributions against quarterly compounding earn four quarters.

How does it handle a 0% rate?

As plain arithmetic, never a division by zero. At 0% the annuity formula's denominator is zero, so the calculator uses the count of contributions instead: the balance is the starting amount plus the contribution multiplied by the number of payments. 10,000.00 plus 100.00 a month for 10 years is exactly 22,000.00, with zero interest.

Are the weekly and daily options exact?

They are equal-period approximations, which is worth knowing before you trust the last digits. Weekly means 52 equal periods a year and every two weeks means 26; a calendar year runs about 52.18 weeks, so a real weekly plan slips in an extra payment roughly every six years and this model does not. Daily compounding means 365 periods a year, with no leap-day adjustment.

Is anything I type sent anywhere?

No. The whole calculation is JavaScript running on your own device. There is no account, no rate feed, no currency conversion and no network request of any kind — the currency selector changes the symbol and the digit grouping only. You can disconnect from the internet and the page keeps working.