Past Due Interest
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The follow-up paragraphs cover two methods used in the system for charging the past due interest. When the Payday Loan lending scheme is used, these two methods become similar, since the entire payment schedule consists of one installment and the total outstanding amount of the current installment equals the outstanding balance.
Past due interest charged on the outstanding balance
According to this method, the past due interest is computed daily on the basis of the outstanding balance. The outstanding balance on the first overdue day OB comprises the total outstanding principal amount, interest outstanding as of the current date (i.e. excluding interest outstanding for all next scheduled installments that are not due yet) and, if provided, commission. On the first overdue day (n = 1), the past due interest is calculated as follows: OI1 = OB x DOIR, where DOIR is the daily overdue interest rate. Then, on the same day, the outstanding balance gets updated OB1 = OB + OI1. On the second overdue day (n = 2), the past due interest is charged on the updated outstanding balance OI2 = OB1 x DOIR, whereupon the outstanding balance gets also updated: OB2 = OB1 + OI2. Proceeding with these considerations, we conclude that the past due interest on the n- th overdue day can be calculated by the following formula:
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Thus, formulas (2) and (7) are valid in any case, while formulas (3) – (6) describe only a particular case without late fees and made repayments.
Past due interest charged on the current debt
According to this method, the past due interest is charged daily on the current debt. On the first overdue day, the current debt includes the principal and interest outstanding for the current installment and, if provided, commission.
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In the payment schedule, each overdue installment is charged a corresponding amount of the outstanding debt that has been calculated within the settlement period.
Transforming the overdue interest rate into the daily overdue interest rate
To charge the interest for overdue payments, the monthly late payment interest (the overdue interest rate) is applied in the system, while the arrears of interest are calculated on the basis of the daily late payment interest (the daily overdue interest rate). The daily overdue interest rate can be computed on the basis of the overdue interest rate by the following formula:
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(13)
Updating the outstanding balance
The current paragraph describes the simultaneous calculation of the past due interest, late fees and update of the outstanding balance.
Once the overdue days start, the system charges the predefined past due interest and late fee every day and updates the outstanding balance or the current debt accordingly (i.e. taking into account the past due interest and late fee charged).
Calculation method using the outstanding balance
In case the past due interest is charged on the outstanding balance on the n-th overdue day, taking into account the outstanding balance OBn-1 on the previous n-1-th day, the system makes the following calculations:
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ОBn - outstanding balance (comprising the principal amount, interest, past due interest, late fee and commission) on the n-th overdue day.
Calculation method using the current debt
In case the past due interest is charged on the current debt on the n-th overdue day, the system makes the following calculations:
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If the late grace days are available, the system charges neither the past due interest nor fees during these days. However, once the overdue period exceeds the late grace days, the system charges the past due interest and late fee for all overdue days by using recursive algorithm (14) – (16) or (17) – (20) depending on a method used for calculating the past due interest.
Using formulas (6) and (9) for charging late fees
To calculate the past due interest and late fees, formulas (6) or (9) can be used in addition to recursive algorithms (14) – (16) or (17) - (20). Formulas (6) and (9) or their generalization in case of applying the late grace days (12) are convenient to use for the direct (without recursion) calculation of the past due interest for all n overdue days. However, as described in paragraph 1, these formulas have been derived on condition that only the past due interest is charged for the overdue installment each day, i.e. when deriving formulas (6), (9) it has not been taken into account that late fees can be additionally charged on any overdue days. In case the past due interest and fees are provided for the overdue installment, the outstanding balance and the current debt must be updated every day, taking into account the past due interest and fees charged.
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After that, formula (6) can be used again. Thus, the past due interest charged by the system for all m overdue days taking into account the late fee charged on the k-th overdue day can be calculated as follows:
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The example of charging the past due interest and late fee
Assume a loan has been taken out for 3 months in the amount of 5 000 USD. Late grace days are not available in a credit product, the monthly interest rate equals 1.2 %. The overdue interest rate equals 3%. The percentage of the outstanding balance for charging the late fee on the first and second days equals 2% and 5% correspondingly. The commission amounts to 20 USD.
Initial payment schedule
Suppose that the annuity calculation method is used and the loan origination date is May 18. Then according to the payment schedule calculation rules described in the articles “Annuity” and “/wiki/spaces/TKL/pages/38211”, the initial payment schedule will look as follows:
Installment Number | Principal | Interest | Commission | Total |
June 18 | 1646.83 | 60.00 | 20.00 | 1726.83 |
July 18 | 1666.59 | 40.24 | 20.00 | 1726.83 |
August 18 | 1686.59 | 20.24 | 20.00 | 1726.83 |
Total | 5000.00 | 120.48 | 60.00 | 5180.48 |
Calculating the past due interest and late fee
Let us consider the case when the first installment is 4 days overdue. The installment due date is June 18, i.e. the borrower fails to repay the loan till June 22 inclusive. According to the method of calculating the past due interest on the basis on the current debt, the system charges the past due interest and late fees daily in accordance with formulas (17) – (20). On June 18, the current debt comprises all payments due for the first installment:
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