Appendix J to Part 1026 - Annual Percentage Rate Computations for Closed-End Credit Transactions
12:9.0.1.1.1.9.1.1.10 : Appendix J
Appendix J to Part 1026 - Annual Percentage Rate Computations for
Closed-End Credit Transactions (a) Introduction
(1) Section 1026.22(a) of Regulation Z provides that the annual
percentage rate for other than open-end 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 unit-period
(or fractional unit-period) 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 unit-periods and
fractional unit-periods 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
Rule
The annual percentage rate shall be the nominal annual
percentage rate determined by multiplying the unit-period rate by
the number of unit-periods in a year.
(2) Term of the Transaction
The 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) Unit-Period
(i) In all transactions other than a single advance, single
payment transaction, the unit-period 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 unit-period; or
(B) If there is no common period in the transaction, the
unit-period 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 unit-period.
(ii) In a single advance, single payment transaction, the
unit-period shall be the term of the transaction, but shall not
exceed 1 year.
(5) Number of Unit-Periods Between 2 Given Dates
(i) The number of days between 2 dates shall be the number of
24-hour intervals between any point in time on the first date to
the same point in time on the second date.
(ii) If the unit-period is a month, the number of full
unit-periods between 2 dates shall be the number of months measured
back from the later date. The remaining fraction of a unit-period
shall be the number of days measured forward from the earlier date
to the beginning of the first full unit-period, divided by 30. If
the unit-period is a month, there are 12 unit-periods per year.
(iii) If the unit-period 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
unit-periods and the remaining fraction of a unit-period shall be
determined by dividing such number of days by 15 in the case of a
semimonthly unit-period or by the appropriate multiple of 30 in the
case of a multimonthly unit-period. If the unit-period is a
semimonth, the number of unit-periods per year shall be 24. If the
number of unit-periods is a multiple of a month, the number of
unit-periods per year shall be 12 divided by the number of months
per unit-period.
(iv) If the unit-period is a day, a week, or a multiple of a
week, the number of full unit-periods and the remaining fractions
of a unit-period shall be determined by dividing the number of days
between the 2 given dates by the number of days per unit-period. If
the unit-period is a day, the number of unit-periods per year shall
be 365. If the unit-period is a week or a multiple of a week, the
number of unit-periods per year shall be 52 divided by the number
of weeks per unit-period.
(v) If the unit-period is a year, the number of full
unit-periods 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 unit-period 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 unit-periods in the term shall be 1, and the
number of unit-periods 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 unit-periods in the term shall be
1, and the number of unit-periods per year shall be 365 divided by
the number of days in the term.
(6) Percentage Rate for a Fraction of a Unit-Period
The percentage rate of finance charge for a fraction (less than
1) of a unit-period shall be equal to such fraction multiplied by
the percentage rate of finance charge per unit-period.
