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).
FINANCEConvert 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.
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.
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.