APR vs APY: Two Rates, One Loan, and the Gap Nobody Quotes You
APR ignores compounding. APY ignores fees. Neither is the whole cost, which is why a 24.99% card charges 28.38% and a 6.5% mortgage is advertised at 6.70%. Here is the conversion in both directions with worked numbers.
APR vs APY: What Each One Leaves Out
Both are annual percentages. They answer different questions and each one deliberately omits something. APR annualises a rate without compounding it, but on loans it folds in fees. APY compounds the rate properly, but ignores fees entirely.
The result is that lenders quote APR, banks quote APY, and neither number can be compared directly to the other. This article gives the conversion, the size of the gap at every compounding frequency, and the two places the difference is large enough to matter.
Try the compound interest calculatorSet a rate and a compounding frequency to see the effective annual return the two produce together.What each one actually measures
Swipe sideways to compare columns.
| APR | APY | |
|---|---|---|
| Full name | Annual percentage rate | Annual percentage yield |
| Accounts for compounding | No | Yes |
| Accounts for fees | On loans, yes | No |
| Where you see it | Loans, cards, mortgages | Savings, CDs, money market accounts |
| Also called | Nominal rate | Effective annual rate, EAR |
| Always the larger of the two? | No, smaller when compounding is frequent | Yes, for the same nominal rate |
The asymmetry is not accidental. Lenders disclose APR because regulation requires a fee-inclusive figure. Banks advertise APY because compounding makes the number look larger. Each industry quotes the convention that flatters it, and both are legally correct.
Converting between them
Take a 6% APR and vary only how often it compounds. Nothing about the stated rate changes.
Swipe sideways to compare columns.
| Compounding | Periods per year | APY | On $10,000, one year |
|---|---|---|---|
| Annually | 1 | 6.0000% | $600.00 |
| Semi-annually | 2 | 6.0900% | $609.00 |
| Quarterly | 4 | 6.1364% | $613.64 |
| Monthly | 12 | 6.1678% | $616.78 |
| Daily | 365 | 6.1831% | $618.31 |
| Continuously | infinite | 6.1837% | $618.37 |
Where the gap gets large: credit cards
The gap widens with the rate, not just the frequency, and it widens faster than most people expect. A card advertising 24.99% APR compounds daily on the outstanding balance.
Regulation permits this. Card disclosures use APR, and daily compounding is disclosed in the terms rather than in the headline number. Nothing is hidden, but the number on the front of the offer is not the number you pay.
Try the credit card payoff calculatorSee what a balance actually costs at a given rate and payment, month by month.Where APR is the more honest number: mortgages
On a mortgage the relationship inverts. The advertised APR is higher than the note rate, because it includes origination fees, points, and other closing costs spread across the term. Here APR is the number doing the useful work.
Swipe sideways to compare columns.
| Line | Amount |
|---|---|
| Loan amount | $300,000 |
| Note rate | 6.5% |
| Monthly principal and interest | $1,896.22 |
| Points and lender fees | $6,000 |
| Net cash received | $294,000 |
| APR, the rate that makes $294,000 produce that payment | 6.70% |
The APR calculation assumes you keep the loan for the full term. If you refinance or sell in year five, the fees are spread over five years rather than thirty, and the effective cost is far higher than the quoted APR. On the example above, paying $6,000 to save a quarter point only pays back if you stay long enough, which is a separate calculation from the APR itself.
Try the mortgage points break-even calculatorFind how many months you must keep the loan for paid points to be worth it.On savings accounts, APY is the only number to use
Deposit accounts have no fees folded into the rate, so APY is a complete measure of what you earn. When two banks quote differently, convert before comparing.
Swipe sideways to compare columns.
| Offer | Stated | True APY | On $25,000 |
|---|---|---|---|
| Bank A | 4.35% APY | 4.3500% | $1,087.50 |
| Bank B | 4.30% APR, compounded daily | 4.3936% | $1,098.39 |
Bank B has the lower headline and pays $10.89 more. Small, but the point stands: comparing an APY to an APR is comparing two different quantities, and the lower-looking one can be the better offer.
Try the savings calculatorProject a balance from a rate, a compounding frequency, and a regular contribution.The working rules
- Comparing loans: use APR, because it captures fees. Convert to APY only if you want to know the true compounded cost of carrying a balance.
- Comparing deposits: use APY. If a bank quotes APR, convert it up before comparing.
- Comparing a loan to an investment return: convert both to APY. This is the only apples-to-apples basis.
- Any quote without a compounding frequency is incomplete. Ask for it.
- On loans you pay off quickly, APR overstates the fee spread and the real cost is higher.
- A rate above about 15% is where the APR to APY gap becomes large enough to change a decision.
What this does not tell you
- Neither rate captures behaviour. A card at 28.38% effective costs nothing if you clear the statement balance every month, because the grace period means no interest accrues at all.
- Mortgage APR calculations vary in which fees lenders include. Two lenders quoting the same APR may have included different costs, so ask for the itemised list.
- Variable rates make both figures a snapshot. A card APR tied to a prime rate changes when that rate changes, and today APY on a savings account is not a commitment.
- APY on savings is pre-tax. In a taxable account, a 4.39% APY at a 24% marginal rate is 3.34% after tax, which is the number to compare against a loan rate.
- The mortgage APR above assumes the full 30-year term. Almost nobody keeps a mortgage that long, so the figure systematically understates fee cost for the typical borrower.
- Introductory rates distort everything. A 0% APR for twelve months followed by 26.99% has no single meaningful annual rate.
Which is higher, APR or APY?
For the same nominal rate on a deposit, APY is always higher or equal, because it compounds. On a loan with fees, the quoted APR is higher than the note rate for the opposite reason: it adds cost the note rate leaves out. The two comparisons are not the same comparison.
How do I convert 18% APR to APY?
Compounded monthly, (1 + 0.18/12)¹² − 1 = 19.56%. Compounded daily, (1 + 0.18/365)³⁶⁵ − 1 = 19.72%. The frequency matters more the higher the rate goes.
Why is my mortgage APR higher than my interest rate?
Because it includes points, origination fees, and certain closing costs amortised across the loan term. A 6.5% note rate with $6,000 of fees on $300,000 comes to roughly 6.70% APR. If your APR equals your note rate, the loan had essentially no lender fees.
Does daily compounding really matter on a savings account?
Barely. At 4% on $25,000, moving from monthly to daily compounding earns about $1.60 more per year. Compare the rate itself, then the fees and minimum balance rules, and treat compounding frequency as a tiebreaker.
Is APY the same as effective annual rate?
Yes. Effective annual rate, EAR, and annual equivalent rate are the same quantity as APY. APY is the term used in consumer deposit disclosure; EAR is the term used in finance textbooks.
My card says 24.99% APR. What do I actually pay per day?
The daily periodic rate is 24.99% divided by 365, or 0.06847% a day, applied to the balance. Because yesterday's interest joins today's balance, a full year of that compounds to 28.38% rather than 24.99%.
Written by
Do The Calculation Team
Do The Calculation
Do The Calculation is built by a small team of data analysts and spreadsheet developers. Where a guide depends on a published formula, standard, or government rule, the calculator it links to names that source directly so you can check the number yourself.
About the team