Interest Short-term Individual Loan
Item General introduc tion / Role in Simfi
Description This formula is used to calculate the interest charges on short term loans of three months, given to the MFIÂ´s clients. Although the math is straightforward, the actual calculation might present some difficulties. The three-month loan serves as an example for all short term and long term loans that behave in a similar way.
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The formula is simple enough:
Monthly Interest Rate Individual Loans: this amount is given on a monthly basis to make the calculations simpler. Monthly interest rates can be converted to annual interest rates using the following formula:
The interest is calculated on a monthly basis. So, within a three month reporting period of the simulation, three interest calculations are carried out. However, the interest does not accrue. The interest amount does not vary and stays with the loan cohort till redemption. The interest is due at the end of the month and is calculated before the loan pay-back takes place. However, defaulted loans do not pay interest. Probability of default (per year) individual loans: this rate is given on a yearly basis. Annual PDs can be converted to monthly PDs using the following formula:
Defaults take place at the end of the month. No interest will be calculated or paid for defaulted loans. Pay back rate: this pay-back rate is determined by the duration of the loan. On three-month loans, 1/3 of the principal is paid back at the end of the month. Calculations
At the end of the month, the amount subject to interest charges is calculated after the deduction of defaults and redemptions. This becomes complicated for the paybacks, since previous defaults have to be compensated for.
Loans Started Loans 1JanQ1
Loans 1JMarQ1 Total New 1,000.00 1,000.00 Table 1: Three loan cohorts starting at the first of each month
We consider one decision period of a quarter or three months. Every month, a new loan cohort of 1,000.00 is initiated, in order to show the transgression from one month to the next one. The first and last dates of the months are listed separately. Monthly Interest Loans 1JanQ1 1.00% Loans 1JFebQ1 1.00% Loans 1JMarQ1 1.00% Table 2: Monthly interest and redemptions
Monthly Redemption 33.33% 33.33% 33.33%
The interest calculation excludes the loans that have defaulted. The defaulted loan amounts are given in the table below: Defaults 1JanQ1 31JanQ1 1FebQ1 28FebQ1 1MarQ1 Loans 1JanQ1 50.00 50.00 Loans 1JFebQ1 50.00 Loans 1JMarQ1 Totals 50.00 100.00 Table 3: Defaults occur at the end of each month (data are given and not calculated)
31MarQ1 50.00 50.00 50.00 150.00
Totals 150.00 100.00 50.00 200.00
At the end of every month, the pay-back amount or redemption is calculated. Redemption 1JanQ1 31JanQ1 1FebQ1 Loans 1JanQ1 316.67 Loans 1JFebQ1 Loans 1JMarQ1 Totals 316.67 Table 4: Three loan cohorts starting at the first of each month
28FebQ1 291.67 316.67
31MarQ1 241.67 291.67 316.67 850.00
For instance, the amount in table 4 under Loans1JanQ1 at the end of January equals 316.67. This pay-back amount is calculated by taking the initial loan amount of 1,000.00, subtracting the default of 50.00 that occurred on 31JanQ1 and dividing this by three.
If we move to the next month, to 28FebQ1, the calculation becomes as follows:
The intuitive reasoning behind these factors, is that for the default that occurred in January for the Loans1JanQ1 cohort, the MFI will miss out repayment on three occasions: the end of January, February, and March. For that reason the loss needs to be divided by three. The default occurring in February for Loans1JanQ1 cohort can only be deducted on two months: February and March, since January has already passed. Therefore, this factor is then divided by two.
Following the same reasoning, defaults occurring in March for the Loans1JanQ1 cohort will be divided by just one.
Since the interest amount is calculated before pay-back, but after deduction of the defaults, we arrive at the following overview of the amounts subject to interest charges at the end of the month. Subject to Interest charge 1JanQ1 31JanQ1 1FebQ1 Loans 1JanQ1 950.00 Loans 1JFebQ1 Loans 1JMarQ1 Table 5: Amounts subject to interest charges at the end of the month
28FebQ1 583.33 950.00
31MarQ1 241.67 583.33 950.00
For the cohort Loans1JanQ1, the amount for 31JanQ1 is just the 1,000.00 outstanding, minus the 50.00 default.
For the cohort Loans1JanQ1, in finding out the amount for 28FebQ1, the defaults for January and February need to be subtracted as well as the redemption for January. The February redemption is not taken into account yet, since the interest is calculated before pay-back.
The same goes for the amount on 31MarQ1, with three defaults of 50.00 and two redemptions to account for:
Finally, we can calculate the actual interest by multiplying the amount subject to interest charge by the interest rate. Just a reminder: the interest rate is fixed and stays with the loan cohort. Interest charged 1JanQ1 31JanQ1 1FebQ1 Loans 1JanQ1 9.50 Loans 1JFebQ1 Loans 1JMarQ1 Totals 9.50 Table 6: Interest charged at the end of the month
28FebQ1 5.83 9.50 15.33
31MarQ1 2.42 5.83 9.50 17.75
Totals 17.75 15.33 9.50 42.58