# 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.

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- **Canonical URL:** https://dothecalculation.com/blog/finance/apr-vs-apy-comparison
- **Category:** Finance
- **Author:** Do The Calculation Team
- **Published:** 2026-08-03
- **Reading time:** 11 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

---

## 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.

Tool: [Try the compound interest calculator](https://dothecalculation.com/calculators/compound-interest-calculator) — Set a rate and a compounding frequency to see the effective annual return the two produce together.

## What each one actually measures

**The two rates compared**
|  | 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

**APR to APY and back**

```
APY = (1 + APR / n)ⁿ − 1    ·    APR = n × [ (1 + APY)^(1/n) − 1 ]
```
- n is the number of compounding periods per year: 12 for monthly, 365 for daily.
- Use decimals, so 6% is 0.06.
- At n = 1 the two are equal. Every increase in n widens the gap, but with rapidly diminishing effect.

Take a 6% APR and vary only how often it compounds. Nothing about the stated rate changes.

**A 6% APR at different compounding frequencies**
| 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 |

> **Compounding frequency has a ceiling** — The whole distance from annual to infinitely frequent compounding is 18 basis points at a 6% rate. Moving from daily to continuous adds six hundredths of a basis point. A bank advertising "daily compounding" as a feature is selling you $1.53 a year on $10,000 over monthly compounding.

## 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.

**A 24.99% card, compounded daily**

```
APY = (1 + 0.2499 / 365)³⁶⁵ − 1 = 28.38%
```
- Carrying $5,000 for a year at the stated 24.99% would cost $1,249.50.
- At the true 28.38% effective rate it costs $1,418.95.
- The $169.45 difference is compounding that the advertised rate does not show.

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.

Tool: [Try the credit card payoff calculator](https://dothecalculation.com/calculators/credit-card-payoff-calculator) — See 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.

**A $300,000 loan at a 6.5% note rate over 30 years**
| 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% |

> **How to read a mortgage quote** — The note rate sets your payment. The APR tells you what the loan costs once fees are counted. Compare lenders on APR, but budget on the note rate, because the fees are paid at closing and never appear in a monthly statement.

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.

Tool: [Try the mortgage points break-even calculator](https://dothecalculation.com/calculators/mortgage-points-break-even-calculator) — Find 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.

**Two offers that are not what they look like**
| 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.

Tool: [Try the savings calculator](https://dothecalculation.com/calculators/savings-calculator) — Project 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%.

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_Source: [Do The Calculation](https://dothecalculation.com/blog/finance/apr-vs-apy-comparison). Quote freely with attribution and a link to this page._