Compound Interest Calculator
Compound interest with monthly contributions, any compounding frequency, and a year-by-year breakdown.
Enter what you are starting with, anything you add each month, the annual rate and how often interest is added. The calculator shows the final balance, how much of it is interest rather than your own money, and a year-by-year table so you can see the curve steepen.
The compound interest formula
A = P × (1 + r/n)n·t
- P — principal, the amount you start with
- r — annual rate as a decimal (7% → 0.07)
- n — compounding periods per year (1 yearly, 12 monthly, 365 daily)
- t — number of years
- A — the balance at the end; interest earned is
A − P
Monthly contributions are added with the future-value-of-an-annuity formula, PMT × ((1 + i)m − 1) ÷ i, where i is the rate converted to a monthly figure and m is the number of months. Deposits are assumed to land at the end of each month.
Worked example
$10,000 at 7%, compounded monthly, for 10 years, with no contributions:
- r/n = 0.07 ÷ 12 = 0.00583333 per month.
- n·t = 120 months → 1.00583333120 = 2.009661.
- A = 10,000 × 2.009661 = $20,096.61 — the money has doubled.
Add $200 a month and the same decade ends at $54,713.58: $34,000 of your own money and $20,713.58 of interest.
How much does compounding frequency matter?
Less than most people expect. $10,000 at 7% for 10 years:
| Compounded | Balance after 10 years |
|---|---|
| Yearly | $19,671.51 |
| Quarterly | $20,016.12 |
| Monthly | $20,096.61 |
| Daily | $20,136.18 |
Daily beats yearly by about $465 over a decade — real, but small next to the effect of the rate itself or of starting a few years earlier. Rate and time do the heavy lifting.
The Rule of 72
Divide 72 by the annual rate for a quick estimate of the doubling time: at 6% money doubles in roughly 12 years, at 9% in about 8. It is accurate to within a year for rates between about 2% and 12%.
Common mistakes
- Entering the rate as a decimal. Type 7 for 7%, not 0.07.
- Confusing APR with APY. APR is the quoted rate before compounding; APY is what you actually earn after it. 7% APR compounded monthly is 7.23% APY — the figure shown above.
- Assuming a fixed return. A projection at a flat 7% is a useful illustration, not a forecast; markets do not deliver the same number every year.
- Forgetting tax and inflation. Interest is often taxable, and $54,713 in ten years buys less than $54,713 today.
Sources
- US SEC, Investor.gov — Compound interest calculator (used to cross-check the figures above).
- Consumer Financial Protection Bureau — What is compound interest? on APR vs APY.
Related: how to calculate compound interest step by step, compound interest explained, and the simple interest calculator for loans that do not compound.
Frequently asked questions
What is the formula for compound interest?
A = P(1 + r/n)^(nt), where P is the starting amount, r the annual rate as a decimal, n the number of compounding periods per year and t the number of years. The interest earned is A − P.
How do I calculate compound interest with monthly contributions?
Work out the lump sum with A = P(1 + r/n)^(nt), then add the future value of the deposits: PMT × ((1 + i)^m − 1) ÷ i, where i is the monthly rate and m the number of months. This calculator does both and adds them together.
What is the difference between APR and APY?
APR is the stated annual rate before compounding is taken into account; APY (AER in the UK) is the effective rate after it. 7% APR compounded monthly works out to 7.23% APY.
Does compounding daily make a big difference?
Only a small one. On $10,000 at 7% over 10 years, daily compounding returns about $465 more than yearly. The interest rate and the length of time matter far more than the frequency.
Is my data sent anywhere?
No. The calculation runs entirely in your browser; nothing you type is sent to the server.