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 , where 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 , or 13.87%; and if it is compounded monthly, the one-year EAR is 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 twelve 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 ( is greater than ). But for a billing period of 31 days, the order is reversed ( is less than ). 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 twelve billing periods and 365 days. Table 1 below, given by Prosper (2005), shows data from Experian, one of the three main U.S. and UK credit bureaus (along with Equifax in the UK and TransUnion in the U.S. and internationally). (The data actually come from installment loans [closed end loans], but can also be used as a fair approximation for credit card loans [open end loans]). The table shows the loss rates from borrowers with various credit scores. To get a desired rate of return, a lender would add the desired rate to the loss rate to determine the interest rate. Though individual borrowers differ, lenders predict that, as an aggregate, borrowers will tend to exhibit the same payment behavior that others with similar credit scores have shown in the past. Banks