Compound Interest Calculator
Calculate how your money grows when interest compounds, and see how much difference the compounding frequency actually makes. Enter a principal, a rate, and a time frame to compare annual, monthly, daily, and continuous compounding side by side.
Your compound interest results will appear here
Enter your principal, rate, and time, then click calculate.
Quick Answer
Compound interest is A = P(1 + r/n)^(nt), where n is how many times per year interest is added. This calculator runs annual, monthly, daily, and continuous compounding side by side, and more frequent compounding always produces a slightly higher balance for the same nominal rate.
How It Works: Formula & Variables
A = P(1 + r/n)^(n·t)
- P (Principal)
- The starting balance.
- r (Rate)
- The nominal annual interest rate, as a decimal.
- n (Frequency)
- How many times per year interest compounds: 1 for annual, 12 for monthly, 365 for daily.
- t (Time)
- The number of years the balance grows.
Continuous compounding: A = P × e^(rt). Effective APY: (1 + r/n)^n − 1.
Source: SEC, Investor.gov Compound Interest Calculator, which uses the same formula and offers annual, semiannual, quarterly, monthly, and daily compounding.
Worked Examples
Example: $5,000 at 4% for 3 years, by compounding frequency
Annually: $5,624.32 ($624.32 interest). Monthly: $5,636.36 ($636.36 interest). Daily: $5,637.45 ($637.45 interest). Continuous: $5,637.48. Each step up in frequency adds a little more, but the gains get smaller each time.
Key Concepts
Compounding frequency matters less than people assume: The jump from annual to monthly compounding is noticeable, but monthly versus daily barely changes the outcome on most account balances and time frames.
The nominal rate and the effective rate aren't the same thing: A bank might advertise 4% and mean the nominal rate before compounding, or the APY after compounding. Knowing which one you're looking at matters when comparing offers.
U.S. savings accounts almost always use APY: Since APY already bakes in the compounding, it's the number to compare across banks, rather than trying to guess each bank's underlying compounding schedule.
Common Mistakes
Ignoring compounding frequency entirely: Two accounts both advertised at "5%" won't grow at exactly the same rate if one compounds monthly and the other compounds daily.
Confusing the nominal rate with APY: Treating an advertised nominal rate as if it were already the effective annual yield leads to slightly underestimating how much a balance will actually grow.
Forgetting to convert time periods: The rate needs to be divided by n, and the number of years needs to be multiplied by n, before plugging either into the formula. Skipping either step throws off the whole calculation.
Frequently Asked Questions
Compound interest is interest calculated on both the principal and on any interest that's already been added to the balance. That's what gives it an accelerating curve instead of a flat, straight-line increase.
Simple interest grows in a straight line using A = P(1 + rt). Compound interest grows faster because each period's interest gets added to the balance before the next period's interest is calculated, using A = P(1 + r/n)^(nt). On $5,000 at 4% over 3 years, simple interest earns $600, while monthly compounding earns $636.36.
Yes, though the gain shrinks as you compound more often. Going from annual to monthly compounding makes a bigger difference than going from monthly to daily. On $5,000 at 4% over 3 years, annual compounding reaches $5,624.32, monthly reaches $5,636.36, and daily reaches $5,637.45.
It's the mathematical limit of compounding more and more often, calculated as A = P x e^(rt). In practice it earns only a few cents more than daily compounding on most balances, but it's a useful reference point.
A quick way to estimate how long it takes money to double: divide 72 by the interest rate. At 6%, for example, 72 / 6 = 12, so your balance roughly doubles in 12 years.
APY is the effective annual rate after compounding is applied, calculated as (1 + r/n)^n - 1. A 4% nominal rate compounded monthly, for instance, works out to a slightly higher APY once the compounding is accounted for.
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