APR to APY Calculator

APR vs APY: the complete guide

Walk into any bank and you will encounter two sets of numbers for the same product: one on the savings side and a different one on the loan side. Banks advertise APY on savings accounts to make returns look higher, and APR on loans to make costs look lower. Understanding the difference lets you compare products honestly and avoid being misled by marketing.

What is APR?

APR stands for Annual Percentage Rate. It is the simple annual interest rate expressed as a percentage, without accounting for the effect of compounding within the year. If a loan has an APR of 12%, that means 12% of the outstanding balance is charged as interest per year — or 1% per month in the case of monthly compounding.

For loans, the Truth in Lending Act (TILA) requires lenders in the United States to disclose APR. For mortgages, APR includes not just the interest rate but also origination fees, points, and certain closing costs — making it a more complete measure of borrowing cost than the simple interest rate alone.

What is APY?

APY stands for Annual Percentage Yield. It is the effective annual rate after accounting for compounding — interest earning interest on itself throughout the year. If a savings account compounds monthly at a 5% APR, you do not earn exactly 5% by year end; you earn slightly more because each month's interest is added to the principal and earns interest the next month. That slightly higher effective rate is the APY.

The formula is: APY = (1 + APR/n)^n − 1, where n is the number of compounding periods per year. For daily compounding, n = 365. For monthly, n = 12. For quarterly, n = 4. The more frequently interest compounds, the higher the APY relative to APR.

Why compounding frequency matters

At low interest rates and over short time periods, the difference between APR and APY seems trivial. But over longer periods and at higher rates, it becomes significant. Consider $100,000 at 5% APR:

• Annual compounding: 5.000% APY → $5,000 earned in year 1
• Monthly compounding: 5.116% APY → $5,116 earned in year 1
• Daily compounding: 5.127% APY → $5,127 earned in year 1

The difference of $127 in the first year does not sound dramatic. But compounding is exponential — the advantage grows over time. Over 30 years, that same $100,000 grows to $448,000 at 5% APR with annual compounding versus $449,000 with daily compounding. The gap widens further at higher rates.

Which rate does your bank advertise — and why?

For savings accounts, banks advertise APY. This is both legally required (under the Truth in Savings Act) and strategically motivated — APY is always higher than or equal to APR, so it makes returns look better. When comparing high-yield savings accounts or CDs, use APY as the apples-to-apples comparison.

For loans and credit cards, lenders advertise APR. For credit cards, the APR is effectively the daily periodic rate multiplied by 365 — there is no compounding in the traditional sense because interest is applied to the outstanding balance each billing cycle. For mortgages, personal loans, and auto loans, the APR is the nominal rate, which you can convert to APY using this calculator to understand the true annual cost.

Practical applications

When comparing two savings accounts, always use APY. Account A might offer 5.00% APR compounding monthly (5.12% APY), while Account B offers 5.05% APR compounding quarterly (5.17% APY). Despite Account A having a lower stated APR, Account B delivers a higher actual return. Use the compound interest calculator to project the dollar difference over time.

For loans, the APR is your comparison point — it is standardized and legally required. But to truly understand your monthly cost, convert to APY and compare. For a personal loan at 9% APR compounding monthly, the effective APY is 9.38% — meaning you are paying nearly 9.4% per year in true cost, not 9.0%.