**
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.