Description of Installment Loan Calendar Systems
Actual-over-365 (US Rule)
The actual-over-365 method counts the number of days in the first
period (between the loan date and the first payment due date),
and then computes the first period interest charge by applying
1/365th of the annual rate for each day in the first
period. Interest is accrued using the U.S. Rule.
For each subsequent month, the actual number of days is counted
between each payment due date and the next, and the interest charge
for the period is computed by applying 1/365th of the annual rate
for each day within the period (28, 29, 30 or 31 days).
This method is considerably harder to calculate. It provides a
slightly more precise payment than the Actual-to-first or Federal Calendar
methods, but the gain in precision does not materially improve the
accuracy of the payment and is usually of little value for these
Payments often cannot be made on their exact due date because
of weekends, holidays, etc.,
Borrowers are often early or late in making the payments, and
The actual interest charge is assessed on a day-by-day basis
based on the days the actual payments are made. This
means that the final payment will nearly always be different
than the regular payment due to these variations in the
Thus, even when an exact payment is computed by this method, the
borrower would still end up with an odd, final payment.
To check loans that were written with this method, we suggest you
use the Actual-to-first method.
Actual-to-First-Payment (US Rule)
The actual-to-first method counts the number of days between the
loan date and the first payment due date, and then computes
the first period interest charge by applying 1/365th of the annual
rate for each day in the first period. Interest is accrued
using the U.S. Rule.
For each subsequent month, interest is charged by applying 1/12th of
the annual rate to the balance due during the month. (This
results in an average interest charge for 30.4166667 days per
This method can be used to compute the payments for both
simple-interest and pre-computed
This method produces a payment and interest charge very close to the
theoretical payment computed by the Actual-over-365
method but without the complexity of that method. The APR
can be disclosed either by the U.S. Escrow Rule by the Federal
"Federal" Calendar (US Rule / Actuarial)
The "Federal" calendar is the method described in U.S. Federal
Reserve Regulation Z to measure the first period for the actuarial
method of computing the Annual Percentage Rate. This method is
commonly used by recent software vendors, mostly because it is
published. It is well suited for pre-computed loans, however for simple-interest
loans, the Actual-to-first or Actual-over-365 method would be preferred. Interest is
accrued using the U.S. Rule or a
However the Federal calendar's intended purpose was to be used to
calculate the A.P.R. by the Actuarial method,
and not as a method to charge interest. Under Regulation Z,
lenders have the choice of using the actuarial method or the U. S.
Escrow Rule to disclose the A.P.R. Regulation Z clearly states
that is has no authority over the charging of interest -- that is a
matter for the states to regulate. Because a majority of
states require the use of the U. S. Escrow
Rule to compute and charge interest on consumer loans (that is,
the charging of interest on unpaid interest is not allowed), it
makes more sense to use either the Actual-to-first or Actual-over-365
calendar systems to compute and disclose consumer loans.
(The U.S. Escrow Rule prevents the charging of interest on unpaid
interest, which can occur when a loan has a first period that is
longer than one month. Unpaid interest is held aside in an
escrow account, and no additional interest is charged upon it.
In contrast, the actuarial method simply adds unpaid interest to the
principal amount, allowing it to negatively amortize. This
results in additional interest charges accruing on the unpaid
One interesting feature of the Federal calendar is that it always
computes 1 month to the first payment if the loan and first payment
due date fall on the same day of the month. E.g., February
15th to March 15th is considered 1 month, as is March 15th to April
15th. For a simple-interest loan, these first periods would be
28 (in a non-leap year) days and 31 days, resulting is a
significantly different interest charge for the first period
(see note 2).
Other Calendar Systems
In commercial lending (which is not subject to Regulation Z), it is
common to see an Actual over 360 calendar system. This system
uses a daily rate that is 1/360th of the annual rate, and then
assesses that rate for all 365 days in the year.
This results in an extra 5 days' interest for the lender.
effectively increasing the interest rate. E.g., a 12.5% loan
on this calendar system will net the lender an actual rate of
Also, the old 360-day year calendar is occasionally found, mostly in
commercial lending. This system assumes every month has 30
days, and charges 1/360th of the annual rate per day.
If a loan has no odd-days in the first period, i.e., the loan date
and first payment due date are 1 month apart, this calendar system
will give the same result as the Federal
calendar. However, if there is a short or long first
period, the 360-day year calendar is not acceptable for assessing an
interest charge or disclosing the A.P.R.
Which Calendar Method Should Be Used?
It depends on whether you are calculating loans or verifying loans
that have already been calculated, and also on what the type
of loan is (simple-interest or pre-computed).
To calculate the payment for simple-interest loans, the most
accurate payment will be calculated by the Actual-over-365 or Actual-to-first
methods, although as noted above the payment will not be materially
more accurate. The actual-to-first method is sometimes
preferred because the results are consistent from one month to
another when the number of days to the first payment is the
same. The method is also far simpler to compute. The
results are very close to the Actual-over-365
method. (Furthermore, Regulation Z states that one can
ignore the fact that months have a different number of days when
To calculate the payment for pre-computed
loans, the most common method in use is the Federal calendar (mostly because the formulae are
published in Regulation Z). For indirect loans, you will find
the Federal calendar is much more commonly used,
however the actual-to-first method will provide a
more accurate count of the days in the first period (resulting in a
more accurate interest charge). Also, pre-computed loans are
much more common in indirect lending.
We note that in early 2005, GMAC switched to a simple-interest
method for their auto loans abandoning the pre-computed method they
had been using for years.
If you are verifying loans from an indirect (or direct) source, you
should probably use the same method that was used to compute the
loan. If you use another method, you will see small
differences in the payment and A.P.R. These differences are
not really differences in the A.P.R., but are caused by the
variations in the way the lengths of the periods are measured and
the effect upon the calculated payment. The A.P.R. is a
time-value measure of the cost of borrowing, and it is affected by
both the Finance Charge and the amount of time the borrower has the
use of the money.
Pre-Computed vs. Simple-Interest Loans
With a pre-computed loan, if the borrower makes all the scheduled
payments on time, he has fulfilled the loan. If the borrower
is late past the end of a grace period (typically 10 days) the
lender can assess a late charge, however, no additional interest is
charged. Thus the interest charge has been "pre-computed" and
will not change.
Simple interest loans charge the borrower one day's interest for
each day the loan is outstanding. The interest is computed for
each day between one payment and the next.
Pre-computed loans were commonly called Rule-of-78 loans by older
loan processing systems because the pre-computed interest was
accrued a month at a time using the Rule of 78's. (Using the
Rule of 78's is no longer allowed in nearly all, if not all,
However, one can still have pre-computed loans and use the Actuarial
method to accrue the interest charges. Today, it is common to
have such pre-computed loans. The pre-computed interest is commonly
apportioned a month at a time using an actuarial method (1/12th of
the annual rate is applied to the balance to compute the interest
for the month). If a borrower elects to pay off the loan in
the middle of a payment period, the lender is required to compute a
payoff amount that only charges the borrower for the actual number
of days that have elapsed in the period.
Actuarial Method: When used to compute an A.P.R., the
actuarial method will result in either the same or slightly lower
percentage than the U.S. Escrow Rule (thus making it slightly less
stringent on lenders). The actuarial method was probably
adopted for this reason, as well as because it is easier to
calculate than the U.S. Rule method. Only the formulae for the
actuarial method are published in Regulation Z.
However, when the actuarial method formulae are "turned-around",
that is, used to compute the interest charge rather than the A.P.R.,
the resulting charge can be higher than that developed with the U.S.
Note 2: States with simple-interest laws typically
specify that only 1 day's interest can be charged for each day
(24-hour period). Use of the Federal calendar to charge
interest can result in 2, 3 or more days of interest being charged
for one day.
For pre-computed loans with one month to
the first period, use of the Federal calendar is usually accepted.