APR vs APY: The Critical Difference That Costs You Money

What APR and APY Actually Measure

The Annual Percentage Rate (APR) and the Annual Percentage Yield (APY) are the two annualized interest metrics most commonly disclosed to US consumers. They look similar, sound similar, and are routinely confused — at measurable cost to borrowers and depositors who choose products by the wrong one.

The APR is the cost of borrowing, annualized, including certain fees required to originate the loan. It is the figure lenders must disclose on consumer credit under the Truth in Lending Act (TILA, 15 U.S.C. §1601) and its implementing Regulation Z (12 CFR Part 1026). APR is the right number to compare when shopping installment loans, credit cards, mortgages, and auto loans.

The APY is the effective annual return on a deposit, reflecting the effect of intra-year compounding. It is the figure banks and credit unions must disclose on savings accounts, money market accounts, and certificates of deposit under Regulation DD (12 CFR Part 1030), which implements the Truth in Savings Act. APY is the right number to compare when shopping deposit accounts.

The APR is what you pay; the APY is what you earn. Confusing the two systematically overstates the value of deposits and understates the cost of debt.

The Mathematical Relationship

If a deposit account pays a nominal annual rate r compounded n times per year, the APY is:

APY = (1 + r/n)^n − 1

For a savings account paying 5.00% nominal compounded monthly, APY = (1 + 0.05/12)^12 − 1 = 1.004167^12 − 1 ≈ 5.116%. The APY exceeds the nominal rate because each month's interest earns interest in subsequent months.

For a loan, the APR calculation begins with the nominal interest rate and then adds certain required fees — origination fees, discount points, mortgage insurance premiums on certain loans — spread across the loan term using the actuarial method specified in Regulation Z (12 CFR §1026.22). The APR on a 30-year mortgage at 6.75% nominal with \$3,000 of origination fees and points on a \$300,000 loan might come out to roughly 6.89% APR — about 14 basis points above the nominal rate.

Critically, the APR for an installment loan does not include the effect of intra-year compounding, because installment loans do not compound in the same way deposit accounts do. Each payment retires principal, so interest accrues only on the declining balance. The APR reflects the effective annual cost of the loan's interest and certain fees, not the compounded yield.

Worked Comparison: A Loan versus a Deposit

Suppose a credit union offers a 5-year personal loan at 8.00% nominal interest, with a \$200 origination fee on a \$10,000 principal. The monthly payment using the amortization formula is \$202.76/month × 60 months = \$12,165.60 total paid. Subtracting the \$10,000 principal leaves \$2,165.60 in total interest and fees.

To compute APR under Reg Z, the origination fee is treated as reducing the net loan proceeds to \$9,800, and the rate is solved for the equivalent amortization that produces the same \$202.76 payment on \$9,800 of net proceeds. The result: roughly 8.74% APR. The APR exceeds the nominal rate because the \$200 fee is amortized across the 60-month term.

Now compare a 5-year certificate of deposit at 5.00% nominal interest, compounded monthly. The APY is 5.116%, as computed above. The CD grows \$10,000 to \$10,000 × (1.004167)^60 = \$12,833.59 over 5 years — \$2,833.59 of interest earned.

If you are evaluating whether to pay down the loan or fund the CD, the relevant comparison is 8.74% APR (cost of debt) versus 5.116% APY (return on deposit). The 364 basis point gap means the borrower is mathematically better off paying down the loan — each dollar of prepayment saves 8.74% of interest, while each dollar of deposit earns 5.116%. The 5.116% is also taxable as ordinary income (or grows tax-deferred in a retirement account), while the 8.74% loan prepayment is risk-free and tax-equivalent.

Reg Z Tolerances and Disclosure Rules

Regulation Z (12 CFR §1026.22) does not require the disclosed APR to match the calculated APR exactly. Tolerances are allowed for rounding and for the complexity of certain fee calculations:

• Regular transactions: tolerance of 1/8 of 1 percentage point (12.5 basis points)
• Irregular transactions: tolerance of 1/4 of 1 percentage point (25 basis points)

An "irregular transaction" is one with irregular payment intervals, irregular payment amounts, or irregular first-period intervals (such as a mortgage with a 45-day first period rather than the standard 30-day). Most consumer mortgages are regular; some private auto loans and personal loans are irregular.

If the disclosed APR exceeds the tolerance, the lender is in violation of TILA and may face civil liability under 15 U.S.C. §1640 — statutory damages of \$100-\$1,000 per violation, plus actual damages and attorney's fees for individual actions, plus class-action damages capped at the lesser of \$500,000 or 1% of the creditor's net worth.

When Each Number Appears

• Mortgages. The Loan Estimate and Closing Disclosure required by the TILA-RESPA Integrated Disclosure rule (12 CFR §1026.37 and §1026.38) display both the interest rate and the APR on the front page. The APR appears in the "Loan Terms" table; the interest rate appears in the "Project Payments" table.
• Credit cards. The Schumer Box (named after Senator Chuck Schumer, who championed the 1988 amendment) requires that credit card solicitations display the APR for purchases, balance transfers, and cash advances prominently. Variable-rate cards must also disclose the index and margin used.
• Auto loans. Disclosed on the retail installment contract; APR must appear in the Federal Truth in Lending box near the signature line.
• Savings accounts and CDs. The "Truth in Savings" disclosure box required by Reg DD shows the APY, the interest rate, the compounding frequency, and any minimum balance requirements.
• Money market accounts. Same Reg DD disclosure regime as savings accounts.

Common Sources of Confusion

• "The rate is 5% — is that APR or APY?" In advertising, "rate" is ambiguous. Banks marketing deposits tend to mean nominal rate (which understates yield); lenders marketing loans tend to mean nominal rate (which understates cost). Always ask which figure is being quoted and ask for the APY on deposits and the APR on loans.
• Continuous compounding. The limit of (1 + r/n)^n as n grows without bound is e^r, where e is the base of natural logarithms (approximately 2.71828). At a 5% nominal rate, continuous compounding yields APY = e^0.05 − 1 = 5.127%, versus 5.116% for monthly compounding. The difference is negligible at typical consumer rates.
• APR on credit cards. Credit card APRs are typically quoted as variable rates indexed to Prime, with a margin based on the cardholder's credit profile. The Schumer Box must also disclose penalty APRs that may apply after late payments.
• "0% APR" promotions. A 0% APR financing offer on a car or appliance is technically the cost of credit, not the cost of the product. Often, the buyer gives up a cash rebate in exchange for the 0% financing; the implicit cost of the forgone rebate should be amortized across the loan term and added to the comparison.
• Mortgage APR understates the cost of discount points. Discount points are prepaid interest: 1 point equals 1% of the loan amount, paid upfront to reduce the nominal rate. The APR calculation amortizes points across the full loan term, but most mortgages are refinanced or paid off within 7-10 years — so the effective APR is higher than the disclosed APR for borrowers who move early.

Conclusion

APR and APY are the same nominal rate viewed through different compounding lenses. APR is the right number for comparing consumer credit because it includes the fees the borrower must pay. APY is the right number for comparing deposits because it captures the effect of intra-year compounding on the yield. Comparing an APR to an APY — or comparing either to a nominal rate — is the single most common arithmetic mistake consumers make when shopping financial products.

Cross-check any APR you are quoted against our APR Calculator and any APY against our Compound Interest Calculator.

This article is for educational purposes only and does not constitute financial or lending advice. Loan and deposit terms vary by institution and borrower profile. See our disclaimer for full terms. Written by the HT99 Tools Editorial Team.