What is APR?
APR is the yearly interest rate on a loan or credit card, expressed as a simple percentage. On many loans, such as mortgages and personal loans, the APR also folds in certain upfront fees, like origination fees or points, spread over the life of the loan. That is why a loan's APR is often higher than its note rate.
What APR does not show is compounding. A credit card with a 24% APR doesn't charge 24% once a year; it charges a periodic rate (for example 2% a month) on your balance. If unpaid interest is added to the balance, you end up paying interest on interest.
What is APY?
APY is the rate you actually earn on savings over one year once compounding is included. If a bank pays interest monthly, each month's interest starts earning interest the next month, so the yearly result is a little more than the stated rate.
APY is the number to use in the savings calculator, and it lets you compare accounts that compound daily, monthly or quarterly on equal terms.
How do you convert APR to APY?
APY = (1 + r/n)ⁿ − 1
Where r is the yearly rate as a decimal and n is the number of times interest compounds per year (12 for monthly, 365 for daily). To go the other way, from APY to a periodic rate, use r = n × ((1 + APY)^(1/n) − 1).
- Take a 6% rate compounded monthly: r = 0.06, n = 12.
- Find the monthly rate: 0.06 ÷ 12 = 0.005.
- Compound it for a year: 1.005¹² ≈ 1.06168.
- Subtract 1: APY ≈ 0.06168, or 6.17%.
This conversion uses the interest rate only. A loan APR that includes fees isn't a pure compounding rate, so applying the formula to it gives the effective yearly rate on that APR, not a figure lenders publish.
APR to APY at common rates
| Stated rate | Quarterly | Monthly | Daily (365) |
|---|---|---|---|
| 1% | 1.004% | 1.005% | 1.005% |
| 2% | 2.015% | 2.018% | 2.020% |
| 3% | 3.034% | 3.042% | 3.045% |
| 4% | 4.060% | 4.074% | 4.081% |
| 5% | 5.095% | 5.116% | 5.127% |
| 6% | 6.136% | 6.168% | 6.183% |
| 8% | 8.243% | 8.300% | 8.328% |
| 10% | 10.381% | 10.471% | 10.516% |
| 15% | 15.865% | 16.075% | 16.180% |
| 20% | 21.551% | 21.939% | 22.134% |
| 24% | 26.248% | 26.824% | 27.115% |
At savings-account rates the difference is a few hundredths of a percentage point. At credit card rates it is several points. For a deeper look at how frequency affects a balance over many years, see the compound interest calculator.
Why do lenders quote APR and banks quote APY?
In the US, federal disclosure rules require lenders to state the APR on consumer credit and banks to state the APY on deposit accounts. Each figure is standardized for its purpose: APR lets you compare the cost of credit including certain fees, and APY lets you compare savings accounts that compound differently.
There is also a presentation effect. The APR on a monthly-compounding loan is lower than its effective yearly cost, and the APY on a savings account is higher than its stated rate. Both numbers look better for the institution quoting them, which is one more reason to compare like with like.
How fees change a loan's APR
Say you borrow $10,000 for 36 months at a 9% interest rate, and the lender deducts a $300 origination fee, so you receive $9,700. The monthly payment on $10,000 is about $318.00, and total interest is about $1,447.90. You can check that payment with the loan EMI calculator.
Because you only received $9,700 but still repay $318.00 a month, the true cost is higher than 9%. Solving for the rate that makes 36 payments of $318.00 worth $9,700 gives an APR of about 11.09%. That is the number to compare against a rival loan with no fee.
What should you compare when choosing an account or loan?
- Savings accounts: compare APY. An account paying 4.90% compounded daily has an APY of about 5.02%, which beats a 5.00% APY account, even though its stated rate is lower.
- Loans: compare APR for the same term and loan type, and check whether each APR includes the same fees.
- Credit cards: the APR understates the cost if you carry a balance. A $1,000 balance at 24% APR compounded monthly grows to about $1,268.24 in a year if you make no payments and no other charges apply.
- Simple-interest products: some loans and bonds don't compound at all. There, the stated rate is the yearly cost; see the simple interest calculator.
Rates, fees and terms vary by lender and by your credit profile, so the right choice depends on your personal circumstances. The examples above use hypothetical rates.