APR Calculator (APR ↔ APY + True Loan APR)

Convert APR ↔ APY at any compounding frequency, plus true APR on a loan after fees and points (Regulation Z disclosure).

FINANCE

Convert between APR (Annual Percentage Rate) and APY (Annual Percentage Yield) at any compounding frequency, and compute the "true APR" on a loan after origination fees and discount points - the figure lenders must disclose under the Truth in Lending Act (Regulation Z). APR is the standard for loans; APY is the standard for savings; the gap grows with compounding frequency.

APY = (1 + APR/n)^n - 1 where n is compoundings per year. Continuous compounding: APY = e^APR - 1. A 6% APR compounded monthly becomes 6.17% APY. For loans, the Truth in Lending Act requires lenders to disclose the "true APR" that bakes in lender fees - a 6.0% note rate with $5,000 in fees on a $300,000 30-year mortgage works out to approximately 6.14% true APR. The calculator uses Newton's method to solve the inverse amortization equation for the unknown APR.

Disclaimer: For loans, true APR depends on which fees are includable per Regulation Z - lenders may interpret differently. For savings, banks may quote APR or APY; always confirm which before depositing.

APR Calculator (APR to APY and Effective Rate)

Convert between APR (Annual Percentage Rate) and APY (Annual Percentage Yield) with different compounding frequencies. Also computes the true APR on a loan after fees and points - the number lenders are required to disclose under Regulation Z.

Mode

Nominal Rate (%)The stated interest rate, before compounding effects.

Compounding Frequency

APY

6.1678%

APR6.0000%

APY6.1678%

Difference (APY - APR)0.1678%

The gap grows with compounding frequency and rate.

APR vs APY - Why the Difference Matters

APR (Annual Percentage Rate) is the stated annual interest rate before compounding. APY (Annual Percentage Yield) is the effective rate after compounding within a year. A 6% APR compounded monthly equals 6.17% APY. APR is the standard for loans (credit cards, mortgages, auto loans); APY is the standard for savings (HYSA, CDs). The conversion: APY = (1 + APR/n)^n - 1, where n is compounding periods per year.

For loans, Truth in Lending Act (Regulation Z) requires lenders to disclose an "APR" that includes most fees (origination, points, broker fees) - not just the interest rate. This "true APR" is always higher than the note rate. A 6.0% note rate with $5,000 in fees on a $300,000 30-year mortgage works out to a true APR around 6.14%. Compare loans by true APR, not just by quoted rate.

Continuous compounding is the mathematical limit as n → infinity: APY = e^APR - 1. For practical rates (under 10%), continuous compounding only adds ~0.05% over daily compounding. For investments, an extra 0.1-0.2% APY/APR difference compounds dramatically over 20-30 years - which is why "no-fee" funds (Vanguard, Fidelity index funds at 0.03% expense ratio) outperform high-fee actively managed funds (1%+ expense ratio) over time.

For loans, the true APR depends on which fees are includable per Regulation Z - lenders may interpret differently. For savings, banks may post APY or APR; always confirm before depositing.

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Frequently Asked Questions

What is the APR Calculator (APR ↔ APY + True Loan APR) for?

How do I use the APR Calculator (APR ↔ APY + True Loan APR)?

How accurate are my apr (apr ↔ apy + true loan apr) results?

For loans, true APR depends on which fees are includable per Regulation Z - lenders may interpret differently. For savings, banks may quote APR or APY; always confirm which before depositing.

Is the APR Calculator (APR ↔ APY + True Loan APR) free to use?

Yes - every calculator on WhichCalc is completely free with no signup, no usage limits, and no tracking on the calculation itself. Results display instantly in your browser and your inputs are never sent to a server. Bookmark the page if you use this calculator regularly.

APR Calculator (APR ↔ APY + True Loan APR)

APR Calculator (APR to APY and Effective Rate)

APR vs APY - Why the Difference Matters

Frequently Asked Questions

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APR Calculator (APR to APY and Effective Rate)

APR vs APY - Why the Difference Matters