Compound Interest Rate Calculator
From principal, final balance and years, solve the compound annual rate (with continuous compounding supported).
Input Data
Results
At a glance:Given PV, FV, years and frequency, solve the rate. Discrete: r = m x ((FV/PV)^(1/(m·t)) - 1); continuous: r = ln(FV/PV)/t; EAR = (1+r/m)^m - 1 (or e^r - 1). Example: 1,000 → 2,000 in 10y annual → ≈7.18% nominal and EAR. KEY: same FV/years always gives the same EAR regardless of frequency; nominal falls as frequency rises. WARNING: PV, FV > 0; compare on EAR. Education, not advice.
Formula
Discrete (periodic) rate: r = (FV / PV)^(1 / n) − 1.
Continuous rate: r = ln(FV / PV) / T, where T is time in years.
$$$r=m\\left(\\left(\\dfrac{FV}{PV}\\right)^{\\frac{1}{mt}}-1\\right)$$$$$$r=\\dfrac{\\ln(FV/PV)}{t}$$$$$$EAR=\\left(1+\\dfrac{r}{m}\\right)^{m}-1$ () $EAR=e^{r}-1$ ()$$How to Use
- Enter the initial principal and final balance.
- Enter the years and pick the compounding frequency.
- View the nominal rate and EAR.
FAQ
What is the difference between nominal rate and EAR?
Nominal rate ignores compounding effect; EAR reflects the true annual return after compounding. Higher frequency makes EAR exceed the nominal rate more noticeably.
What is continuous compounding?
It assumes interest is reinvested at every instant — the limit as frequency → infinity, using e. It is the theoretical upper bound of compounding and the basis of many finance models (e.g. derivatives pricing).
Why must principal and balance be positive?
Solving the rate requires taking the root or log of FV/PV; zero or negative values are mathematically invalid for a meaningful compound rate.
How does this differ from normal compound calculation?
Normal compound calc is forward (known rate → FV). This is reverse (known PV, FV, years → rate). Very useful when you have 'invested X, ended with Y, over N years' (a fund, policy or business) and want the annualised return. Mathematically it needs the FV/PV ratio rooted (discrete) or logged (continuous), hence positivity required.
Why is the continuous nominal rate lowest — is it the best?
Not better — just a different quote. Higher frequency means stronger compounding, so a lower nominal rate achieves the same FV. Continuous is the limit, so its nominal is lowest. But the EAR is identical across frequencies for the same FV/years, because EAR reflects the real return set by the outcome. Always compare on EAR, not nominal. Continuous is a theoretical cap; real products use discrete compounding.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.