The Devil is in the Dates
by Tim Langeman
When we receive loan data from microfinance institutions that wish to become transparent, they enter the information about their loans into our Data Collection Tool. In addition, we always ask for real repayment schedules for active loans given to real borrowers. We use these repayment schedules to verify the information the MFI has entered into our Data Collection Tool, but they also serve another purpose.
You may think you know how many days are in a year or how many weeks in a month, but the answer is not always straightforward. The following examples show some cases where slight variations between loan terms and the actual dates in a repayment schedule can significantly impact the APR.
Sometimes the definition of different repayment frequencies can actually affect the APR. For example, two loans with stated terms of “one year” can actually vary in duration by a few days. By some definitions, a year is composed of twelve 30-day months. (30 days/month * 12 months= 360 days/year). A 360 day “yearly loan” will have a slightly different interest rate than a 365 day “yearly loan”, all else being equal.
Stated repayment frequency is not regular
Loans advertised as having a monthly repayment frequency sometimes in fact require payments every 4 weeks. If you consider a month to be every 4 weeks, then there are 13 months in the year (365/(7*4)=13.03). This means that paying every 4 weeks, the borrower makes 13 payments in the year, whereas if payments were made once a month they would only make 12 payments. This difference affects the APR, but it does not affect the EIR when calculated using the more exact XIRR formula. For an analysis of this discrepancy using a real life example, see the article The Challenge of Understanding Pricing of Microloans.
Actual payment dates are not regular
In some cases, a loan with a weekly repayment frequency will have a payment scheduled every 7 days for the entire loan term. In other cases, payments may be 7 days apart, then 5, then 6, then 7 again, in the same loan term. Payment dates can vary due to holidays or other factors. The payment date might also vary by a few days because of a weekend. With some loans, it is also possible for the first payment of a monthly loan to take place less than 1 month from the disbursement date. These slight changes are accurately reflected in the more exact XIRR formula, but are not picked up by the traditional IRR formula used to calculate the APR.
Interest rates are a complex and interesting subject. It can be difficult to know just how significant a few days here and there can be when calculating the true cost of a loan. If you haven’t already, take the opportunity to download and experiment with the Calculating Transparent Prices Tool. Then explore my earlier article describing How to Calculate Interest Rates in Excel, using both the IRR and XIRR approaches. Are there any other quirks about repayment dates that you’ve noticed? How might they factor into APR and EIR calculations?