The following paragraphs contain some notes regarding Reg Z compliance and how these compliance issues relate to some interest calculations in NLS.

From Reg Z: Background and Summary provided by the Federal Reserve (page 14)

If the consumer borrows $2,500 for a vacation trip at 14 percent simple interest per annum and repays that amount with 25 equal monthly payments beginning one month from consummation of the transaction, the monthly P + I payment will be $115.87, if all months are considered equal, and the amount financed would be $2,500. If the consumer’s payments are increased by $2.00 a month to pay a non-financed $50 loan fee during the life of the loan, the amount financed would remain at $2,500 but the payment schedule would be increased to $117.87 a month, the finance charge would increase by $50, and there would be a corresponding increase in the APR. This would be the case whether or not state law defines the $50 loan fee as interest.

If the loan above has 55 days to the first payment and the consumer prepays interest at consummation ($24.31 to cover the first 25 days), the amount financed would be $2,500 - $24.31, or $2,475.69. Although the amount financed has been reduced to reflect the consumer’s reduced use of available funds at consummation, the time interval during which the consumer has use of the $2,475.69, 55 days to the first payment, has not changed. Since the first payment period exceeds the limitations of the regulation’s minor irregularities provisions (see 226.17(c)(4)), it may not be treated as regular. In calculating the APR, the first payment period must not be reduced by 25 days (i.e., the first payment period may not be treated as one month).

Reg Z 226.17 (c)(4)

(4) In making calculations and disclosures, the creditor may disregard any irregularity in the first period that falls within the limits described below and any payment schedule irregularity that results from the irregular first period:
(i) For transactions in which the term is less than 1 year, a first period not more than 6 days shorter or 13 days longer than a regular period;
(ii) For transactions in which the term is at least 1 year and less than 10 years, a first period not more than 11 days shorter or 21 days longer than a regular period; and
(iii) For transactions in which the term is at least 10 years, a first period shorter than or not more than 32 days longer than a regular period.

In practice, the interpretation of what constitutes a long first period, and how that first period is to be accrued has an effect on the payoff balance during any day within that first period. This is important if we do not pre-pay the excess interest, because now we have an irregularly lengthened period. This is not a problem for a simple interest loan but has ramifications on loans with pre-computed interest methods (Fixed Am and rule of 78s).

If the loan in question is simple interest, then the daily accrual would simply be applied for 55 days.

However, if the loan is calculated based on the Fixed Amortized or one of the Rule of 78s Interest methods, the concept of equal periods is inherent to the mathematics of those interest methods. Therefore, the “stub period interest,” 25 days accrual in this case, generally accrued at a ACT/360 basis, must be capitalized, before the first full period of 30 days is accrued.

In the above example: ($2,500 x .14)/360 x 25 = 24.31 (the same figure that we showed above).

Since in this extended example, this is not being pre-paid, it is capitalized, and the principal accrued on for the first full month is: $2,500 + $24.31 = $2,524.31.

One month’s interest is then accrued on this figure: ($2,524.31 x .14)/12 = $29.45.

The total interest for the 55 day period is given by: $24.31 + $29.45 = $53.76.

And so the interest to principal breakdown for the first payment would be $53.76 to interest and $62.11 to principal, reducing the principal balance to $2,437.89 for the start of the second period.

If we had not had an extra 25 days in the first period, the first period interest would have been $29.17 and the principal in the first period would have been reduced by $86.70. Clearly, in order to avoid the generation of a balloon on this loan, the monthly payment would have to be increased slightly to account for the extra 25 days, and this is the reason why pre-paying the stub interest greatly simplifies the situation.

See also Reg Z Tolerance