APR states the annual cost of borrowing without compounding the rate itself; APY states the effective one-year return after a stated compounding schedule. A 5.00% APR compounded monthly produces a 5.116% APY, while a $10,000 loan at 5.00% APR still needs its fees and payment schedule to reveal its total cost.
apr vs apy: the measured relationship
APR is an annualized borrowing rate, while APY is the one-year yield after interest is compounded. APY changes when the crediting frequency changes even if the nominal APR remains 5.00%. APR versus APY is therefore a borrowing-cost-versus-deposit-yield comparison, not a contest between two labels on the same mortgage offer.
| Quoted annual rate | 5.00% APR |
|---|---|
| Compounding periods | 12 per year |
| Effective annual yield | 5.116% APY |
| Starting balance | $10,000 |
apr vs apy: a worked dollar case
Put $10,000 in an account quoted at 5.00% APR with monthly compounding. The monthly rate is 0.05 ÷ 12 = 0.0041667. After 12 monthly credits the balance is $10,511.62, so the annual percentage yield is 5.1162%. A loan advertisement using 5.00% APR answers a different question: it is a standardized annual borrowing measure, not a promise that the balance grows by 5.1162%.
apr vs apy: calculation method
For an account, APY = (1 + APR ÷ m)^m − 1, where m is compounding periods per year. For a loan comparison, keep the quoted APR beside the amount financed, payment count, and disclosed charges; compounding alone cannot recreate every loan disclosure.
compoundingledger related calculations: Savings growth calculator; loan-payment calculation; APR calculator.
Common mistakes in APR vs. APY: what is the difference?
Do not divide a 5.00% APY by 12 and call the result the monthly rate. The monthly rate that compounds to 5.116% is slightly lower than 5.116% ÷ 12. Also do not use a savings APY to infer credit-card interest; the account agreement controls how a card accrues interest.
Where this calculation stops
This example assumes the rate, balance, and monthly compounding stay unchanged for 12 months. It excludes taxes, withdrawal limits, promotional-rate expiry, deposit timing, loan fees, and any rate that can change. A bank statement or loan disclosure is the controlling record.
apr vs apy: source check
The Consumer Financial Protection Bureau explains that APR is a broader measure of borrowing cost than a loan interest rate; its terminology page defines the mortgage context. Read the named source. The compoundingledger record should be reconciled to the disclosure, statement, tax bill, or agreement that governs that exact transaction.
apr vs apy: using the output
The compoundingledger output keeps each input's named unit and date adjacent to the result. Update the compoundingledger scenario when its rate, balance, payment, or property value changes.