How Compound Interest Works
Compound interest is interest earned on both your original principal and on the interest that has already accumulated. Because interest is continually added back to the balance, growth accelerates the longer money stays invested — often described as "interest on interest."
The standard formula for a lump sum with no further contributions is:
Where A is the future value, P is the principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years. When you add regular monthly contributions, this calculator simulates the balance month by month, adding each contribution before applying that month's growth, then converts the nominal annual rate into an effective monthly rate based on your chosen compounding frequency.
Future Value vs. Annualized Return
This calculator reports two different "rate" figures because they answer different questions:
Effective annual rate (EAR) converts your nominal annual rate into the true annual rate implied by the compounding frequency you selected — for example, 6% compounded monthly behaves like roughly 6.17% compounded once a year.
Annualized return (money-weighted) is the internal rate of return (IRR) of every cash flow in and out of the account: your initial deposit, every monthly contribution, and the final balance. Because it weighs the timing of your contributions, it can differ slightly from the EAR — especially when you contribute steadily over a long period.
Frequently Asked Questions
What is compound interest?
Compound interest is interest calculated on both the initial principal and the interest that has already accumulated, so growth accelerates over time compared to simple interest.
What is the compound interest formula?
A = P(1 + r/n)^(nt). With regular contributions, the calculation becomes a series sum on top of this formula, which is what this calculator simulates month by month.
What is annualized return?
It expresses total growth as an equivalent constant yearly rate. This tool reports the money-weighted (IRR) version, which accounts for the timing and size of every contribution.
How does compounding frequency affect returns?
More frequent compounding (daily vs. monthly vs. annually) produces a slightly higher effective annual rate for the same nominal rate, since interest starts earning interest sooner.
Is this calculator financial advice?
No. It provides estimates for educational purposes only and does not account for taxes, fees, inflation, or investment risk. Consult a licensed financial advisor before making decisions.
Disclaimer: This calculator is for educational and illustrative purposes only. It does not constitute financial, investment, tax, or legal advice, and results are estimates that do not account for fees, taxes, inflation, or market risk. Past or projected performance is not a guarantee of future results.