Interest on your interest, compounded as often as you like, with the year-by-year breakdown.
| Year | Paid in | Interest that year | Total interest | Balance |
|---|
A = P(1 + r/n)nt. P is the starting amount, r the annual rate written as a decimal, n how many times a year interest is added, and t the number of years. Compounding daily sets n to 365, monthly sets it to 12, annually sets it to 1.
Each compounding step credits interest on the interest already credited. That is the whole of the difference between compound and simple interest.
Simple interest is always calculated on the original deposit. Put $10,000 in at 7% and it pays $700 a year, every year, forever. After 20 years you have $24,000.
Compound interest is calculated on the deposit plus everything it has already earned, so the base grows and each year pays more than the last. The same $10,000 at 7% compounded annually reaches $38,697 over the same 20 years. The gap is $14,697, and all of it comes from interest that itself earned interest.
Frequency matters much less than the rate or the time horizon. Switching from annual to daily compounding on the same 7%, $10,000, 20-year example only moves the result from about $38,697 to $40,547, a difference of under 5%.
Change the frequency selector and watch the effective annual rate reported above it instead: 7% compounds to an effective 7.23% a year at monthly frequency and 7.25% at daily, which is the one number that captures the whole effect.
Yes, and over shorter periods the contributions usually account for more of the balance than the interest does. Each contribution starts compounding from the month it is added, so the money you put in first spends the longest growing.
The year-by-year table shows where the two cross over. Set a starting amount of 0 and a monthly contribution, and watch the "interest that year" column climb past what you pay in annually. How long that takes depends entirely on the rate and the size of the starting balance.
At 7% compounded annually, 10.24 years. The quick mental version is the Rule of 72: divide 72 by the rate and you get 10.3 years, which is close enough for most purposes. The Rule of 72 calculator shows the estimate and the exact figure side by side.
No. Everything here is the raw arithmetic of a fixed rate. Tax on interest or gains is not included, fund and account fees are not included, and the rate you enter does not shrink to reflect inflation over the period.
Compound interest is interest that earns interest. The formula is A = P(1 + r/n)nt, where P is the starting amount, r is the annual rate written as a decimal, n is how many times a year interest is added, and t is the number of years. Simple interest would pay the same amount every year on the original deposit. Compound interest pays on the deposit plus everything the deposit has already earned, so each year's interest is larger than the last.
Compounding frequency matters less than people expect. At 7% on $10,000 for 20 years, compounding once a year gets to about $38,697 and compounding every day gets to about $40,547. That is a gap of roughly 4.8% after two decades. Adding one percentage point to the rate, or five years to the term, moves the result far more. The frequency gap widens at higher rates and shrinks at lower ones.
Monthly contributions are handled separately from the compounding schedule. This tool converts your chosen frequency into an effective annual rate first, so a rate compounded daily becomes the equivalent annual figure, then applies that rate month by month as contributions arrive. Each contribution is added at the end of its month and starts earning from the following one. With no contributions the result matches A = P(1 + r/n)nt exactly.
The year-by-year table separates what you paid in from what the interest added, which shows the point where the two cross over. With a large starting balance that happens in the first year. With small contributions and a long horizon it can take a decade or more.