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Example #1 - No Odd Days

Example #2 - With Odd Days

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The dealer reserve is calculated by the "Difference in Charges" method, which is the most common.  We have specified the Federal Calendar to measure the first period to make sure that it is exactly one month long.

Input dialog showing entered values

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In the difference-in-charges method, a second, hypothetical loan is calculated using the lender's "buy" rate of 8.90%.  The finance charge on this hypothetical loan is the amount that the lender would retain if 100% of the dealer reserve were paid to the dealer (see below).

The purpose of calculating the lender's retention first is to make sure the lender receives the correct amount even if there are minor errors in the original contract.  For example, if the original payment were 0.05 too low, the contract finance charge would be lower than the correct amount for the stated interest rate.  However, a small difference such as this is not usually enough to warrant rejecting the contract because it won't put it out of Regulation Z tolerance.  By calculating the lender's retention first, the lender will receive the proper amount and the portion paid to the dealer will be slightly less because of the incorrect payment on the original contract.

The exactly-correct lender's retention is subtracted from the contract finance charge to determine the dealer reserve (assuming 100% is paid to the dealer).

In order to compensate the lender for early terminations, it is common to pay less than 100% of the dealer reserve to the dealer.  Thus the above dealer reserve is adjusted by the paid-to-dealer percentage (75% in this case) to determine the actual amount paid to the dealer.

The dealer advance is the sum of the note amount and the actual dealer reserve amount.

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The dealer reserve is calculated by the "Difference in Charges" method, which is the most common.  We have specified the Federal Calendar to measure the first period.  In this loan, the first period is 1 month + 13 days long.

Input dialog showing entered values

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In the difference-in-charges method, a second, hypothetical loan is calculated using the lender's "buy" rate of 5.90%.  The finance charge on this hypothetical loan is the amount that the lender would retain if 100% of the dealer reserve were paid to the dealer (see below).

The calculated lender's retention is subtracted from the contract finance charge to determine the dealer reserve (assuming 100% is paid to the dealer).

In order to compensate the lender for early terminations, it is common to pay less than 100% of the dealer reserve to the dealer.  Thus the above dealer reserve is adjusted by the paid-to-dealer percentage (75% in this case) to determine the actual amount paid to the dealer.

The dealer advance is the sum of the note amount and the actual dealer reserve amount.

Calculating the payment 
with odd-days

None of the readily-available financial calculators such as the HP-12C can calculate a payment properly for a loan with a long first period.

On the right, we show the method to calculate 43 days of simple interest in the first period, and then 30 days (based on a 360-day year) for the remaining periods.

These formulas assume there is no negative amortization of the loan.  (There is no negative amortization in this example.)  The purpose of this example is to show the dealer reserve calculation therefore we have used the simplest calendar system to avoid complicating the calculation method.

See calendar systems and U.S. Rule for details on other methods.   

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Let  i = 5.90 / 1200.0
  Days = 43
     n = 60
  Note = 12053.85
    An = (1 - 1 / ((1 + i) ^ n) / i
   Add = An * (1 + i)

Then,
Pmt = Note x (1 + Days / 30 * i) / Add
    = 12053.85 x 1.00704722 / 52.10511107
    = 232.967475

WARNING:  This formula is only valid for loans with long-first periods that do not negatively amortize.  See U.S. Rule for details on negative amortization.

The payment calculation by the U.S. Rule is far more complicated but is required by most states.   PROM's programs such as the LoanMaker 523A PC and LoanMaker 623A Handheld products use the U.S. Rule in payment calculations.

To properly amortize this loan, one would take 43 days of interest when the first payment is made, and then 30 days (1/12th of a year) for each remaining payment.

Updated 18 Nov 2002

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