APR vs APY

1. Compounding: The Core Distinction

APR is a simple interest rate that doesn't account for how frequently interest compounds. It's calculated as the periodic interest rate multiplied by the number of periods in a year. For example, a credit card charging 1.5% monthly interest has an APR of 1.5% × 12 = 18%. This is a straightforward linear calculation that ignores the fact that unpaid interest accumulates and generates its own interest.

APY accounts for compounding — the effect of earning interest on previously earned interest (or paying interest on unpaid interest). The more frequently interest compounds (daily, monthly, quarterly), the higher the APY relative to the APR. The formula is: APY = (1 + r/n)^n - 1, where r is the nominal rate and n is the number of compounding periods per year.

Example: A 5% interest rate compounded annually equals 5.00% APY. The same 5% compounded monthly becomes 5.12% APY. Compounded daily, it's 5.13% APY. Over time, these small differences accumulate significantly.

2. Where Each Term is Used: Borrowing vs Saving

APR is primarily used for borrowing products where you pay interest. Credit cards, personal loans, auto loans, and mortgages all advertise APR. Federal law (Truth in Lending Act) requires lenders to disclose APR to allow consumers to compare costs. For mortgages, APR includes not just the interest rate but also certain fees (origination fees, points, mortgage insurance), making it a more comprehensive cost measure.

APY is used for savings and investment products where you earn interest. Banks advertise APY on savings accounts, high-yield savings accounts, certificates of deposit (CDs), and money market accounts. Federal regulations require banks to disclose APY (not just APR) so consumers can accurately compare earning potential across different accounts and compounding frequencies.

Marketing Insight: Lenders advertise lower-looking APRs to make borrowing costs appear smaller. Banks advertise higher-looking APYs to make savings accounts appear more attractive. Both tactics use the compounding effect to their advantage in marketing.

3. The Math: How to Calculate Each

APR Calculation: APR = (Interest paid per period) × (Number of periods per year). It's a straightforward multiplication. For a loan charging $50 interest monthly on a $1,000 balance, the monthly rate is 5%, so APR = 5% × 12 = 60%. This doesn't account for the compounding of unpaid interest.

APY Calculation: APY = (1 + r/n)^n - 1, where r is the nominal interest rate (as a decimal) and n is the compounding frequency per year. For 5% compounded daily: APY = (1 + 0.05/365)^365 - 1 = 0.05127 = 5.127%. The more frequent the compounding (larger n), the higher the APY.

Real Example: A savings account advertises "5% interest compounded daily." The APR is 5%, but the APY is 5.13%. If you deposit $10,000, you'll earn $513 in the first year, not $500, due to daily compounding where each day's interest earns interest the next day.

Compounding Frequencies:

• Annual: n = 1 (compounds once per year)
• Quarterly: n = 4 (every 3 months)
• Monthly: n = 12 (every month)
• Daily: n = 365 (every day)
• Continuous: n approaches infinity (maximum theoretical compounding)

4. Impact on Your Money Over Time

APR understates the true cost of borrowing or the true benefit of saving when compounding is involved. A credit card with 18% APR compounded monthly actually costs 19.56% APY — you're paying 1.56 percentage points more than the advertised rate suggests. For borrowers, ignoring compounding can lead to underestimating debt growth. For savers, it means missing out on understanding the true earning potential.

APY gives you the accurate, real-world number that accounts for compounding. It's the effective annual rate — the actual percentage your balance will grow (savings) or shrink (debt) over one year. When comparing financial products, APY provides apples-to-apples comparisons even if compounding frequencies differ.

10-Year Impact Example: Investing $10,000 at 6% APR (no compounding) grows to $16,000 after 10 years. The same $10,000 at 6% APY (compounded monthly) grows to $18,194 — an extra $2,194 due to compounding. Over 30 years, the difference is even more dramatic: $28,000 (simple) vs $60,226 (compound) — more than double.

5. How to Use Each for Comparing Offers

APR is useful for comparing loans with similar structures and payment schedules. When shopping for a mortgage or auto loan, compare APRs to see which lender offers the best deal. However, be aware that mortgage APRs include fees, so a lower rate with high fees might show a higher APR than a slightly higher rate with low fees. Always compare APR to APR, not interest rate to APR.

APY is the gold standard for comparing savings accounts, CDs, and money market accounts. If Bank A offers 4.5% APY and Bank B offers 4.6% APY, Bank B will earn you more money, period — even if Bank A compounds more frequently. APY already factors in compounding frequency, so it's a direct comparison. Always choose the highest APY for savings products.

Comparison Scenario: Bank A: "5.00% interest, compounded annually" (APY = 5.00%). Bank B: "4.90% interest, compounded daily" (APY = 5.02%). Despite Bank A advertising a higher rate, Bank B actually pays more because of daily compounding. The APY reveals Bank B is the better choice.