What is the formula for Effective Annual Rate (EAR)?

The formula is `EAR = (1 + r/n)^n - 1`, where `r` is nominal interest rate and `n` is compounding periods per year.

Why is APY higher than APR for the same interest rate?

Because APY factors in compounding interest ('interest on interest'), which increases the effective annual payout on deposits.

What is continuous compounding?

Continuous compounding is mathematical compounding where interest is calculated and added instantaneously at every microsecond, using the formula `EAR = e^r - 1`.

Why do banks advertise APY for savings but APR for loans?

Banks advertise the higher APY figure on savings accounts to appear more lucrative for deposits, and advertise the lower nominal APR on loans to appear cheaper for borrowers.

How do I convert monthly interest rate to APY?

Multiply monthly rate by 12 to get nominal APR, then apply the formula `APY = (1 + monthly_rate)^12 - 1`.

Why is Effective Annual Rate (APY) higher than nominal Annual Percentage Rate (APR)?

APY reflects intra-year interest compounding frequency (daily, monthly, quarterly). Because accumulated interest earns additional interest over time, APY exceeds nominal APR.

Finance & Business Cluster

Effective Interest Rate Calculator (Convert APR to APY / EAR)

Calculate Effective Annual Rate (EAR / APY) from nominal interest rates and compounding periods.

TL;DR: Effective Interest Rate Calculator converts stated nominal rates (APR) into true Effective Annual Rates (EAR/APY) using the compounding formula $\text{EAR} = (1 + r/n)^n - 1$.

Nominal annual rate %

Compounding frequency

What Is the Difference Between Nominal APR and Effective Annual Rate (APY)?

The nominal rate (APR) is the stated annualized interest rate without accounting for intra-year compounding. The Effective Annual Rate (EAR or APY) reflects the true annual return or cost of borrowing after compounding interest is factored in: EAR = (1 + i/n)^n - 1. APY is always greater than or equal to APR.

How to Use the Effective Interest Rate Calculator (APY)

Our Effective Interest Rate Calculator (APY) performs high-precision mathematical operations directly in your browser with zero latency and complete client-side privacy.

Enter the Stated Nominal Interest Rate (APR percentage).
Select the Compounding Frequency (Annually, Semi-Annually, Quarterly, Monthly, Daily, or Continuous).
Click 'Calculate APY' to compute the exact Effective Annual Rate.
Compare the nominal and effective rates to assess true savings yields or borrowing costs.
Use the result to evaluate credit card costs and bank CD offers.

Mathematical Formula & Equations

Calculates the Effective Annual Rate (EAR / APY) taking compounding frequency ($n$) into account from a stated nominal interest rate ($i$).

\[ EAR = \left(1 + \frac{i}{n}\right)^n - 1 \]

Calculation Example

A nominal 10% rate compounded daily ($n = 365$): $$EAR = \left(1 + \frac{0.10}{365}\right)^{365} - 1 = 10.516\%$$

100% Client-Side Privacy & Data Security

All calculations, amortization schedules, variables, and sensitive numerical datasets execute 100% locally in your web browser memory. Your financial, medical, and personal values are never transmitted, logged, or uploaded to any external server.

Frequently Asked Questions

: The formula is `EAR = (1 + r/n)^n - 1`, where `r` is nominal interest rate and `n` is compounding periods per year.
: Because APY factors in compounding interest ('interest on interest'), which increases the effective annual payout on deposits.
: Continuous compounding is mathematical compounding where interest is calculated and added instantaneously at every microsecond, using the formula `EAR = e^r - 1`.
: Banks advertise the higher APY figure on savings accounts to appear more lucrative for deposits, and advertise the lower nominal APR on loans to appear cheaper for borrowers.
: Multiply monthly rate by 12 to get nominal APR, then apply the formula `APY = (1 + monthly_rate)^12 - 1`.
: APY reflects intra-year interest compounding frequency (daily, monthly, quarterly). Because accumulated interest earns additional interest over time, APY exceeds nominal APR.

Cite This Calculator

Need to reference this online calculator in a financial proposal, academic paper, blog post, or classroom curriculum? Copy a citation below.

NexLove.org. (2026). Effective Interest Rate Calculator (APY) [Online Calculation Tool]. https://nexlove.org/tools/effective-interest-rate-calculator

“Effective Interest Rate Calculator (APY).” NexLove.org, 2026, nexlove.org/tools/effective-interest-rate-calculator.

NexLove.org (2026) Effective Interest Rate Calculator (APY). Available at: https://nexlove.org/tools/effective-interest-rate-calculator (Accessed: 2026).

@misc{nexlove_effective_interest_rate_calculator,
  title = {Effective Interest Rate Calculator (APY)},
  author = {{NexLove.org}},
  year = {2026},
  url = {https://nexlove.org/tools/effective-interest-rate-calculator}
}

Embed This Tool

Add the live Effective Interest Rate Calculator (APY) to your own website with this snippet — it loads the real, working calculator in an iframe.

<iframe src="https://nexlove.org/embed/effective-interest-rate-calculator.html" width="100%" height="600" style="border:1px solid #e2e8f0;border-radius:12px" title="Effective Interest Rate Calculator (APY) — NexLove.org" loading="lazy"></iframe>

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