Banks and lenders use two different interest rate figures — APR and APY — and the way they choose which one to advertise is not neutral. Lenders use APR on loans because it makes the borrowing cost appear lower. Banks use APY on savings accounts because it makes the return appear higher. Both figures are calculated from the same underlying interest rate; the difference is whether compound interest within the year is included. Understanding this distinction is worth real money — it affects how you compare credit card offers, savings accounts, mortgages, and certificates of deposit.
The two acronyms stand for Annual Percentage Rate (APR) and Annual Percentage Yield (APY). APR is the annual interest rate without accounting for within-year compounding. APY includes compounding and therefore shows what you actually earn or pay over a full year. For annual compounding, they are the same. For anything more frequent — monthly, daily — APY is always higher than APR. The gap grows as the compounding frequency increases and as the underlying rate increases.
The Formula and the Math
The relationship between APR and APY is deterministic. If you know the APR and the compounding frequency, you can calculate the APY precisely.
APY = (1 + APR/n)n − 1
Where:
APR = annual percentage rate (as a decimal)
n = number of compounding periods per year
Common values of n:
Annual: n = 1 | Semi-annual: n = 2 | Quarterly: n = 4
Monthly: n = 12 | Daily: n = 365
Let us work through a concrete example. Suppose you are quoted 6% APR compounded monthly — a figure you might see on a savings account or a personal loan.
APY = (1 + 0.06/12)12 − 1
= (1 + 0.005)12 − 1
= (1.005)12 − 1
= 1.06168 − 1
= 6.168% APY
If you deposit $10,000 for one year:
At 6% APR (simple): ending balance = $10,600
At 6.168% APY (with monthly compounding): ending balance = $10,616.78
The $16.78 difference is the compounding effect within the year.
On a savings account balance of $10,000, $16.78 sounds trivial. On a $250,000 balance held for 10 years, the compounding effect across the full period is far more substantial. And on debt, the direction flips: monthly compounding on a credit card balance means you owe more than the nominal APR suggests.
Why APR Is Used on Loans (And Why That Matters)
The federal Truth in Lending Act (TILA), administered by the Consumer Financial Protection Bureau, requires lenders to disclose APR on virtually all consumer loans — mortgages, auto loans, credit cards, personal loans. The legislative intent was transparency: give consumers a single, standardized number to compare loan costs. But APR does not include the compounding that happens within the year, so for loans with frequent compounding, the APR understates the true annual cost.
Credit cards are the most important example. Most credit cards compound daily — they calculate interest on your balance every day, not just once a month. A credit card advertised at 22% APR actually costs 24.6% APY when compounded daily:
APY = (1 + 0.22/365)365 − 1
= (1.000603)365 − 1
≈ 1.2460 − 1
= 24.6% APY
On a $5,000 balance carried for one year:
At 22% APR (simple): interest owed = $1,100
At 24.6% APY (actual with daily compounding): interest owed ≈ $1,230
The $130 difference in this example is money that appears nowhere in the advertised APR. This is not a deceptive practice in a legal sense — TILA requires APR disclosure, not APY — but it means borrowers who compare credit cards solely on advertised APR are missing part of the true cost picture. The practical lesson: always ask whether interest compounds daily or monthly, especially on revolving credit products.
For mortgages, the situation is more complex. Mortgage APR under TILA includes not just the interest rate but also certain fees — origination fees, points, and some closing costs — spread over the loan's term. This makes mortgage APR a broader cost measure than the interest rate alone, but it also makes mortgage APR non-comparable to credit card APR. A 7.0% mortgage APR and a 7.0% credit card APR are fundamentally different figures derived by different calculations.
Why APY Is Used on Savings (And How to Read It)
The Truth in Savings Act, enforced by the FDIC and Federal Reserve for member institutions, requires banks to disclose APY on deposit accounts — savings accounts, money market accounts, and certificates of deposit. Banks use APY on savings because it is the higher number: it includes the within-year compounding and therefore shows the actual annual return a depositor earns.
When a bank advertises a high-yield savings account at "5.00% APY," that 5.00% is the true annual return assuming you make no withdrawals and the rate holds constant. You can use this number directly to compare different savings accounts because they all use the same APY calculation methodology. The underlying compounding frequencies may differ (some banks compound daily, some monthly), but the APY figure already accounts for that difference. When comparing savings accounts, APY is the right number to use.
Bank A: 4.80% APR, compounded daily → APY = 4.917%
Bank B: 4.75% APY (as advertised) → APY = 4.75%
Bank A has a higher APR but its APY (4.917%) still beats Bank B (4.75%).
On $20,000 over one year:
Bank A: $20,000 × 4.917% = $983 in interest
Bank B: $20,000 × 4.75% = $950 in interest
Difference: $33/year — meaningful on larger balances.
When the APR-APY Gap Matters Most
The gap between APR and APY is small at low interest rates with infrequent compounding, and large at high interest rates with frequent compounding. This creates a practical hierarchy of situations where you should pay careful attention to the distinction.
High-APR revolving credit is where the APY-APR gap does the most damage. At a 29.99% APR compounded daily — common on store credit cards — the effective APY is approximately 34.9%. On a $10,000 balance, this means you pay $3,490 per year in interest, not $2,999. The compounding effect adds nearly $500 annually.
Long-term savings and CD rates at high yields benefit from APY compounding. A 5-year CD at 5% APR compounded monthly grows your money by 28.34% over five years, not 25%. On $100,000, that difference is $3,340 — money you earn without any additional effort simply because interest is calculated on a growing balance each month.
Short-term, low-rate instruments — like a standard checking account at 0.01% APR — produce a negligible gap. At 0.01% compounded daily, APY is 0.0100005%. The distinction is mathematically real but practically irrelevant.
The clearest rule: when comparing savings accounts or CDs, compare APY to APY. The bank has already done the compounding math for you. When evaluating loan costs, ask for both the APR and the compounding frequency, then calculate the APY yourself if you want to understand the true annual cost. Our Compound Interest Calculator can compute the effect of any compounding frequency on any balance, and our Loan Calculator shows the full monthly payment and total interest cost for any loan. For a deeper look at why compounding frequency creates these differences, see our article on Compound vs. Simple Interest.
A Quick Reference for Common Products
To make the APR vs. APY framework immediately practical, here is how the terms map onto the financial products you encounter most often.
| Product | Rate Disclosed | Typical Compounding |
|---|---|---|
| Credit cards | APR (TILA) | Daily |
| Mortgages | APR (TILA, includes fees) | Monthly |
| Auto loans | APR (TILA) | Monthly |
| Personal loans | APR (TILA) | Monthly |
| High-yield savings accounts | APY (Truth in Savings Act) | Daily or monthly |
| Certificates of deposit (CDs) | APY (Truth in Savings Act) | Daily or monthly |
| US Treasury bonds | Yield / coupon rate | Semi-annual |
The bottom line: APR and APY are both legitimate rate expressions, but they measure different things. APY is always the more complete picture of what you actually earn or owe over a year. When a financial product advertises APR, mentally note that the true annual cost or yield is the APY — and if the product compounds more frequently than annually, APY will be higher than the stated APR.