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.
Audit the APR vs. APY: what is the difference? scenario
compoundingledger timing check. Record Quoted annual rate as 5.00% APR. compoundingledger timing review changes Compounding periods to 12 per year and keeps the unit beside the figure. A compoundingledger timing comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger cash-flow check. Record Compounding periods as 12 per year. compoundingledger cash-flow review changes Effective annual yield to 5.116% APY and keeps the unit beside the figure. A compoundingledger cash-flow comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger rate check. Record Effective annual yield as 5.116% APY. compoundingledger rate review changes Starting balance to $10,000 and keeps the unit beside the figure. A compoundingledger rate comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger balance check. Record Starting balance as $10,000. compoundingledger balance review changes Quoted annual rate to 5.00% APR and keeps the unit beside the figure. A compoundingledger balance comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger disclosure check. Record Quoted annual rate as 5.00% APR. compoundingledger disclosure review changes Compounding periods to 12 per year and keeps the unit beside the figure. A compoundingledger disclosure comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger schedule check. Record Compounding periods as 12 per year. compoundingledger schedule review changes Effective annual yield to 5.116% APY and keeps the unit beside the figure. A compoundingledger schedule comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger threshold check. Record Effective annual yield as 5.116% APY. compoundingledger threshold review changes Starting balance to $10,000 and keeps the unit beside the figure. A compoundingledger threshold comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger payment check. Record Starting balance as $10,000. compoundingledger payment review changes Quoted annual rate to 5.00% APR and keeps the unit beside the figure. A compoundingledger payment comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger property check. Record Quoted annual rate as 5.00% APR. compoundingledger property review changes Compounding periods to 12 per year and keeps the unit beside the figure. A compoundingledger property comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger income check. Record Compounding periods as 12 per year. compoundingledger income review changes Effective annual yield to 5.116% APY and keeps the unit beside the figure. A compoundingledger income comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger insurance check. Record Effective annual yield as 5.116% APY. compoundingledger insurance review changes Starting balance to $10,000 and keeps the unit beside the figure. A compoundingledger insurance comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
compoundingledger term check. Record Starting balance as $10,000. compoundingledger term review changes Quoted annual rate to 5.00% APR and keeps the unit beside the figure. A compoundingledger term comparison recalculates the stated relationship from those two dated inputs, instead of reusing a rounded intermediate amount.
Keep a decision record
compoundingledger timing record. The compoundingledger worksheet pairs Effective annual yield (5.116% APY) with Starting balance ($10,000). A compoundingledger timing decision tests the effect of that pair before adding another assumption. Keep the compoundingledger timing source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger cash-flow record. The compoundingledger worksheet pairs Starting balance ($10,000) with Quoted annual rate (5.00% APR). A compoundingledger cash-flow decision tests the effect of that pair before adding another assumption. Keep the compoundingledger cash-flow source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger rate record. The compoundingledger worksheet pairs Quoted annual rate (5.00% APR) with Compounding periods (12 per year). A compoundingledger rate decision tests the effect of that pair before adding another assumption. Keep the compoundingledger rate source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger balance record. The compoundingledger worksheet pairs Compounding periods (12 per year) with Effective annual yield (5.116% APY). A compoundingledger balance decision tests the effect of that pair before adding another assumption. Keep the compoundingledger balance source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger disclosure record. The compoundingledger worksheet pairs Effective annual yield (5.116% APY) with Starting balance ($10,000). A compoundingledger disclosure decision tests the effect of that pair before adding another assumption. Keep the compoundingledger disclosure source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger schedule record. The compoundingledger worksheet pairs Starting balance ($10,000) with Quoted annual rate (5.00% APR). A compoundingledger schedule decision tests the effect of that pair before adding another assumption. Keep the compoundingledger schedule source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger threshold record. The compoundingledger worksheet pairs Quoted annual rate (5.00% APR) with Compounding periods (12 per year). A compoundingledger threshold decision tests the effect of that pair before adding another assumption. Keep the compoundingledger threshold source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger payment record. The compoundingledger worksheet pairs Compounding periods (12 per year) with Effective annual yield (5.116% APY). A compoundingledger payment decision tests the effect of that pair before adding another assumption. Keep the compoundingledger payment source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger property record. The compoundingledger worksheet pairs Effective annual yield (5.116% APY) with Starting balance ($10,000). A compoundingledger property decision tests the effect of that pair before adding another assumption. Keep the compoundingledger property source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger income record. The compoundingledger worksheet pairs Starting balance ($10,000) with Quoted annual rate (5.00% APR). A compoundingledger income decision tests the effect of that pair before adding another assumption. Keep the compoundingledger income source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger insurance record. The compoundingledger worksheet pairs Quoted annual rate (5.00% APR) with Compounding periods (12 per year). A compoundingledger insurance decision tests the effect of that pair before adding another assumption. Keep the compoundingledger insurance source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
compoundingledger term record. The compoundingledger worksheet pairs Compounding periods (12 per year) with Effective annual yield (5.116% APY). A compoundingledger term decision tests the effect of that pair before adding another assumption. Keep the compoundingledger term source document with the result, because a revised statement, disclosure, assessment, or account term changes the input rather than the arithmetic.
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.