Appendix J--Annual Percentage Rate Computations for Closed-End Credit Transactions
(a) Introduction
(1) Section 226.22(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.
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