Head-to-head
APR vs APY
APR and APY both start from the same nominal rate and then treat compounding differently. APR is the simple annual rate — the number in the contract. APY converts the effect of compounding into an annual figure, so it is always equal to or higher than APR for any compounding frequency above annual.
The gap depends on two things: how often interest compounds, and how high the rate is. At 6% compounded monthly, APY is 6.17% — a gap of 0.17 points. At 24% compounded daily, the gap is over 2.5 points, which is why credit card APRs and APYs look so different.
Which one you should read depends on direction. For money you are earning, APY is the honest number because it is what the balance actually grows by. For money you are borrowing, APR is the number to compare, and in the US it also folds in fees — which is why a mortgage APR can be higher than its note rate even with monthly compounding.
The asymmetry is worth remembering because the same 6% is a good deal in one direction and a mediocre one in the other. As a saver you want the highest APY; as a borrower you want the lowest APR. Reading the wrong one is how a 6% savings account gets compared against a 6% loan and appears to be a wash.
APR
How To Calculate APR
The APR is the interest rate that would produce your loan's cash flows if the fee were rolled into the rate. It answers a fairer question than the advertised nominal rate: what single annual rate, applied to the money you actually received, reproduces the payments you actually make?
APY
How To Calculate APY
The annual percentage yield is what a deposit account actually returns in a year once compounding is counted. Comparing two accounts by their headline rates instead of their APYs is the most common way savers pick the slower one.
How They Differ
| Attribute | APR | APY |
|---|---|---|
| Includes compounding | No — the nominal annual rate | Yes — the effective annual rate |
| Includes fees | Yes, in US lending disclosures | Not usually |
| Formula | Nominal rate × periods (fees added in disclosures) | (1 + r ÷ n)^n − 1 |
| Which is higher | Lower, or equal if compounded annually | Higher, or equal if compounded annually |
| Used for | Loans and credit — what you pay | Savings and deposits — what you earn |
| Regulated disclosure | Yes — Truth in Lending Act (US) | Yes — Truth in Savings Act (US) |
| Best comparison use | Comparing loans with different fee structures | Comparing accounts with different compounding schedules |
The Same Numbers, Both Ways
A 6% nominal rate compounded monthly, on a $10,000 balance.
- Nominal rate
- 6%
- Compounding
- Monthly
- Balance
- $10,000
| Line | APR | APY |
|---|---|---|
| Stated annual rate | 6.00% | 6.00% |
| Compounding counted | No | Yes, 12 times a year |
| Effective annual rate | 6.00% | 6.17% |
| Interest on $10,000 in year 1 | $600.00 | $616.78 |
| Interest on $10,000 over 5 years | $3,000.00 | $3,488.50 |
The 0.17-point gap is $16.78 in the first year and $488.50 over five years. Two accounts quoting the same 6% APR can differ by this much purely because one compounds monthly and the other annually.
When To Use Each
APR
- You are comparing loans, where fees matter as much as the rate.
- You are checking a credit card or auto loan disclosure, where APR is the regulated figure.
- The product compounds annually, in which case APR and APY are identical.
APY
- You are comparing savings accounts or certificates of deposit.
- You want to know how much a balance will actually grow in a year.
- Compounding is more frequent than annual, and you need a single comparable number.
Common Questions
Is a higher APY always better?
For a savings account, yes, assuming the rate holds and the account is otherwise suitable. For a loan, APY is not the standard disclosure — compare APR, which includes fees, rather than APY, which does not.
Why is my mortgage APR higher than the rate I was quoted?
Because US mortgage APR includes origination fees and points, spread across the loan. A 6% note rate with 2 points of fees can show an APR near 6.3%. That is not a different interest rate — it is the cost of borrowing expressed as a rate.
How do I convert APR to APY?
APY = (1 + APR ÷ n)^n − 1, where n is the number of compounding periods per year. For 6% monthly: (1 + 0.005)^12 − 1 = 6.17%. If you do not know n, you cannot convert — the frequency is the missing input.
Does daily compounding make a big difference?
Smaller than people expect. At 6%, monthly compounding gives 6.168% APY and daily gives 6.183% — a gap of 0.015 points. The jump from annual to monthly is the big one; after that it flattens.
What about credit cards quoting 24.99% APR?
That APR already assumes monthly compounding in most US disclosures. The effective annual cost is around 28.1% — a gap of more than three points, which is why carrying a balance is so expensive.
More Comparisons
- Simple Interest vs Compound Interest
Simple interest charges the principal only; compound interest charges the balance. On $10,000 at 5% over 10 years that gap is $1,288.95 — here is where it comes from.
- ROI vs CAGR
ROI measures the whole return; CAGR turns it into a compound annual rate. A 100% return over five years is 20% a year by division but 14.87% a year in reality.
- Markup vs Margin
Markup divides profit by cost; margin divides it by price. The same $20 profit is 50% markup and 33.3% margin — and the gap widens as the rate rises.
Sources
- Truth in Lending Act — Regulation Z, APR disclosures — Consumer Financial Protection Bureau
- Truth in Savings Act — Regulation DD, APY disclosures — Consumer Financial Protection Bureau
- Credit card interest rates and compounding — Board of Governors of the Federal Reserve System
Both methods sit in Finance.