Description of Installment Loan Calendar Systems


Federal Calendar
Other Systems
Which Calendar To Use?

Pre-Computed vs. Simple-Interest Loans

In the calculation of Installment Loans (including Home Equity loans, but not Mortgages), there are three common methods in use to measure the number of days between payments when computing the interest charge and/or Annual Percentage Rate.

Our LoanMaker 23a App
for the iPhone/iPad has all three of these calendar systems.

Download on the App Store.


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 reasons:

  • 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 payment pattern.

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 month.)

This method can be used to compute the payments for both simple-interest and pre-computed loans.

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 Calendar.

"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 simple/actuarial method.

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 interest.)

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 12.674%.

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 making disclosures.)

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, states.)

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. Rule method.

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.