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Electronic Code of Federal Regulations
Title 12: Banks and Banking
Appendix J to Part 1026—Annual Percentage Rate Computations for ClosedEnd Credit Transactions(a) Introduction(1) Section 1026.22(a) of Regulation Z provides that the annual percentage rate for other than openend credit transactions shall be determined in accordance with either the actuarial method or the United States Rule method. This appendix contains an explanation of the actuarial method as well as equations, instructions and examples of how this method applies to single advance and multiple advance transactions. (2) Under the actuarial method, at the end of each unitperiod (or fractional unitperiod) the unpaid balance of the amount financed is increased by the finance charge earned during that period and is decreased by the total payment (if any) made at the end of that period. The determination of unitperiods and fractional unitperiods shall be consistent with the definitions and rules in paragraphs (b)(3), (4) and (5) of this section and the general equation in paragraph (b)(8) of this section. (3) In contrast, under the United States Rule method, at the end of each payment period, the unpaid balance of the amount financed is increased by the finance charge earned during that payment period and is decreased by the payment made at the end of that payment period. If the payment is less than the finance charge earned, the adjustment of the unpaid balance of the amount financed is postponed until the end of the next payment period. If at that time the sum of the two payments is still less than the total earned finance charge for the two payment periods, the adjustment of the unpaid balance of the amount financed is postponed still another payment period, and so forth. (b) Instructions and Equations for the Actuarial Method(1) General RuleThe annual percentage rate shall be the nominal annual percentage rate determined by multiplying the unitperiod rate by the number of unitperiods in a year. (2) Term of the TransactionThe term of the transaction begins on the date of its consummation, except that if the finance charge or any portion of it is earned beginning on a later date, the term begins on the later date. The term ends on the date the last payment is due, except that if an advance is scheduled after that date, the term ends on the later date. For computation purposes, the length of the term shall be equal to the time interval between any point in time on the beginning date to the same point in time on the ending date. (3) Definitions of Time Intervals(i) A period is the interval of time between advances or between payments and includes the interval of time between the date the finance charge begins to be earned and the date of the first advance thereafter or the date of the first payment thereafter, as applicable. (ii) A common period is any period that occurs more than once in a transaction. (iii) A standard interval of time is a day, week, semimonth, month, or a multiple of a week or a month up to, but not exceeding, 1 year. (iv) All months shall be considered equal. Full months shall be measured from any point in time on a given date of a given month to the same point in time on the same date of another month. If a series of payments (or advances) is scheduled for the last day of each month, months shall be measured from the last day of the given month to the last day of another month. If payments (or advances) are scheduled for the 29th or 30th of each month, the last day of February shall be used when applicable. (4) UnitPeriod(i) In all transactions other than a single advance, single payment transaction, the unitperiod shall be that common period, not to exceed 1 year, that occurs most frequently in the transaction, except that (A) If 2 or more common periods occur with equal frequency, the smaller of such common periods shall be the unitperiod; or (B) If there is no common period in the transaction, the unitperiod shall be that period which is the average of all periods rounded to the nearest whole standard interval of time. If the average is equally near 2 standard intervals of time, the lower shall be the unitperiod. (ii) In a single advance, single payment transaction, the unitperiod shall be the term of the transaction, but shall not exceed 1 year. (5) Number of UnitPeriods Between 2 Given Dates(i) The number of days between 2 dates shall be the number of 24hour intervals between any point in time on the first date to the same point in time on the second date. (ii) If the unitperiod is a month, the number of full unitperiods between 2 dates shall be the number of months measured back from the later date. The remaining fraction of a unitperiod shall be the number of days measured forward from the earlier date to the beginning of the first full unitperiod, divided by 30. If the unitperiod is a month, there are 12 unitperiods per year. (iii) If the unitperiod is a semimonth or a multiple of a month not exceeding 11 months, the number of days between 2 dates shall be 30 times the number of full months measured back from the later date, plus the number of remaining days. The number of full unitperiods and the remaining fraction of a unitperiod shall be determined by dividing such number of days by 15 in the case of a semimonthly unitperiod or by the appropriate multiple of 30 in the case of a multimonthly unitperiod. If the unitperiod is a semimonth, the number of unitperiods per year shall be 24. If the number of unitperiods is a multiple of a month, the number of unitperiods per year shall be 12 divided by the number of months per unitperiod. (iv) If the unitperiod is a day, a week, or a multiple of a week, the number of full unitperiods and the remaining fractions of a unitperiod shall be determined by dividing the number of days between the 2 given dates by the number of days per unitperiod. If the unitperiod is a day, the number of unitperiods per year shall be 365. If the unitperiod is a week or a multiple of a week, the number of unitperiods per year shall be 52 divided by the number of weeks per unitperiod. (v) If the unitperiod is a year, the number of full unitperiods between 2 dates shall be the number of full years (each equal to 12 months) measured back from the later date. The remaining fraction of a unitperiod shall be (A) The remaining number of months divided by 12 if the remaining interval is equal to a whole number of months, or (B) The remaining number of days divided by 365 if the remaining interval is not equal to a whole number of months. (vi) In a single advance, single payment transaction in which the term is less than a year and is equal to a whole number of months, the number of unitperiods in the term shall be 1, and the number of unitperiods per year shall be 12 divided by the number of months in the term or 365 divided by the number of days in the term. (vii) In a single advance, single payment transaction in which the term is less than a year and is not equal to a whole number of months, the number of unitperiods in the term shall be 1, and the number of unitperiods per year shall be 365 divided by the number of days in the term. (6) Percentage Rate for a Fraction of a UnitPeriodThe percentage rate of finance charge for a fraction (less than 1) of a unitperiod shall be equal to such fraction multiplied by the percentage rate of finance charge per unitperiod.
