# 12 CFR Appendix F to Part 1026, Optional Annual Percentage Rate Computations for Creditors Offering Open-End Credit Plans Secured by a Consumer's Dwelling

In determining the denominator of the fraction under § 1026.14(c)(3), no amount will be used more than once when adding the sum of the balances subject to periodic rates to the sum of the amounts subject to specific transaction charges. (Where a portion of the finance charge is determined by application of one or more daily periodic rates, the phrase “sum of the balances” shall also mean the “average of daily balances.”) In every case, the full amount of transactions subject to specific transaction charges shall be included in the denominator. Other balances or parts of balances shall be included according to the manner of determining the balance subject to a periodic rate, as illustrated in the following examples of accounts on monthly billing cycles:

1. Previous balance - none.

A specific transaction of $100 occurs on the first day of the billing cycle. The average daily balance is $100. A specific transaction charge of 3% is applicable to the specific transaction. The periodic rate is 1 1/2% applicable to the average daily balance. The numerator is the amount of the finance charge, which is $4.50. The denominator is the amount of the transaction (which is $100), plus the amount by which the balance subject to the periodic rate exceeds the amount of the specific transactions (such excess in this case is 0), totaling $100.

The annual percentage rate is the quotient (which is 4 1/2%) multiplied by 12 (the number of months in a year), i.e., 54%.

2. Previous balance - $100.

A specific transaction of $100 occurs at the midpoint of the billing cycle. The average daily balance is $150. A specific transaction charge of 3% is applicable to the specific transaction. The periodic rate is 1 1/2% applicable to the average daily balance. The numerator is the amount of the finance charge which is $5.25. The denominator is the amount of the transaction (which is $100), plus the amount by which the balance subject to the periodic rate exceeds the amount of the specific transaction (such excess in this case is $50), totaling $150. As explained in example 1, the annual percentage rate is 3 1/2% × 12 = 42%.

3. If, in example 2, the periodic rate applies only to the previous balance, the numerator is $4.50 and the denominator is $200 (the amount of the transaction, $100, plus the balance subject only to the periodic rate, the $100 previous balance). As explained in example 1, the annual percentage rate is 2 1/4% × 12 = 27%.

4. If, in example 2, the periodic rate applies only to an adjusted balance (previous balance less payments and credits) and the consumer made a payment of $50 at the midpoint of the billing cycle, the numerator is $3.75 and the denominator is $150 (the amount of the transaction, $100, plus the balance subject to the periodic rate, the $50 adjusted balance). As explained in example 1, the annual percentage rate is 2 1/2% × 12 = 30%.

5. Previous balance - $100.

A specific transaction (check) of $100 occurs at the midpoint of the billing cycle. The average daily balance is $150. The specific transaction charge is $.25 per check. The periodic rate is 1 1/2% applied to the average daily balance. The numerator is the amount of the finance charge, which is $2.50 and includes the $.25 check charge and the $2.25 resulting from the application of the periodic rate. The denominator is the full amount of the specific transaction (which is $100) plus the amount by which the average daily balance exceeds the amount of the specific transaction (which in this case is $50), totaling $150. As explained in example 1, the annual percentage rate would be 1-2/3% × 12 = 20%.

6. Previous balance - none.

A specific transaction of $100 occurs at the midpoint of the billing cycle. The average daily balance is $50. The specific transaction charge is 3% of the transaction amount or $3.00. The periodic rate is 1 1/2% per month applied to the average daily balance. The numerator is the amount of the finance charge, which is $3.75, including the $3.00 transaction charge and $.75 resulting from application of the periodic rate. The denominator is the full amount of the specific transaction ($100) plus the amount by which the balance subject to the periodic rate exceeds the amount of the transaction ($0). Where the specific transaction amount exceeds the balance subject to the periodic rate, the resulting number is considered to be zero rather than a negative number ($50 − $100 = −$50). The denominator, in this case, is $100. As explained in example 1, the annual percentage rate is 3 3/4% × 12 = 45%.