Most U.S. credit cards are quoted in terms of nominal APR compounded daily, or sometimes (and especially formerly) monthly, which in either case is not the same as the effective annual rate (EAR). Despite the "annual" in APR, it is not necessarily a direct reference for the interest rate paid on a stable balance over one year.
The more direct reference for the one-year rate of interest is EAR. The general conversion factor for APR to EAR is EAR=((1+APR/n)^n)-1, where n represents the number of compounding periods of the APR per EAR period. For a common credit card quoted at 12.99% APR compounded daily, the one year EAR is ((1+.1299/365)^365) -1, or 13.87%; and if it is compounded monthly, the one year EAR is ((1+.1299/12)^12) - 1 or 13.79.
On an annual basis, the one-year EAR for compounding monthly is always less than the EAR for compounding daily. However, the relationship of the two in individual billing periods depends on the APR and the number of days in the billing period. For example, given 12 billing periods a year, 365 days, and an APR of 12.99%, if a billing period is 28 days then the rate charged by monthly compounding is greater than that charged by daily compounding [ .1299/12 is greater than ((1+.1299/365)^28)-1].
But for a billing period of 31 days, the order is reversed (.1299/12 is less than ((1+.1299/365)^31)). In general, credit cards available to middle-class cardholders that range in credit limit from $1,000 to $30,000 calculate the finance charge by methods that are exactly equal to compound interest compounded daily, although the interest is not posted to the account until the end of the billing cycle.
A high U.S. APR of 29.99% carries an effective annual rate of 34.96% for daily compounding and 34.48% for monthly compounding, given a year with 12 billing periods and 365 days.
The more direct reference for the one-year rate of interest is EAR. The general conversion factor for APR to EAR is EAR=((1+APR/n)^n)-1, where n represents the number of compounding periods of the APR per EAR period. For a common credit card quoted at 12.99% APR compounded daily, the one year EAR is ((1+.1299/365)^365) -1, or 13.87%; and if it is compounded monthly, the one year EAR is ((1+.1299/12)^12) - 1 or 13.79.
On an annual basis, the one-year EAR for compounding monthly is always less than the EAR for compounding daily. However, the relationship of the two in individual billing periods depends on the APR and the number of days in the billing period. For example, given 12 billing periods a year, 365 days, and an APR of 12.99%, if a billing period is 28 days then the rate charged by monthly compounding is greater than that charged by daily compounding [ .1299/12 is greater than ((1+.1299/365)^28)-1].
But for a billing period of 31 days, the order is reversed (.1299/12 is less than ((1+.1299/365)^31)). In general, credit cards available to middle-class cardholders that range in credit limit from $1,000 to $30,000 calculate the finance charge by methods that are exactly equal to compound interest compounded daily, although the interest is not posted to the account until the end of the billing cycle.
A high U.S. APR of 29.99% carries an effective annual rate of 34.96% for daily compounding and 34.48% for monthly compounding, given a year with 12 billing periods and 365 days.
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