I think that I understand now one reason why the length of the loan and the number of repayments cannot always agree. The loan that made me understand is this one:
http://www.kiva.org/app.php?page=businesses&action=about&id=72728.
The amounts of the repayments are those that the entrepreneurs really have to pay, which is often not a monthly term. We focus on loans in Senegal (repaid in one payment at the end of the loan) and loans in Cameroon (a 4 month grace period after disbursement) to find non-classical repayment patterns. Many loans, however, will be repaid on a weekly or fortnightly schedule.
I was surprised in my example that the repayments differ from one month to the next, but then I understood that repayments are weekly. The loan is a 16 week loan, which is 4 months. The description says 3 months, but that is a bug. After correction of the bug, the description will correctly display 5 repayments, but it will still be a 4 month loan.
In my example, the loan (together with the grace period and the invoicing and wiring delays) is considered to have been disbursed either on Friday December 5, Saturday December 6 or Sunday December 7.
The amount of the weekly instalment is $4,125 / 16 = $257.8125.
Until December 15, the entrepreneurs must make 1 weekly payment: $257.8125, or rounded to $257.81.
Until January 15, the entrepreneurs must make 4 weekly payments: $1,031.81.
Until February 15, the entrepreneurs must make 5 weekly payments: $1,289.0625, or rounded to $1,289.06.
Until March 15, the entrepreneurs must make 4 weekly payments: $1,031.81.
Until April 15, the entrepreneurs must make 2 weekly payments: $515.625, or rounded to $515.63.
This shows that Kiva displays exactly what happens in the field. Until now we were happy with our machine generated repayment notices, but it was not the real world outside. We have been spoilt, due also to the lack of communication. The new system is thus a
BIG improvement.

Kiva uses now a better word for the repayment dates. As these are the last possible dates, they are called "Due Dates" and not "Expected Dates".

Now I have
2 questions:
- How will Kiva explain to the lenders that a 4 month loan has really 5 repayments when the repayments are computed by weeks and not whole months, whenever the loan does not start at the beginning of the month? It is in this case not a bug, but it must be properly explained, otherwise contactus will be swamped by misled lenders or, worse, potential lenders will walk away as they don't trust the system.
- Often, at least in my part of the world, borrowers pay the same amount for each instalment. In the beginning, the remaining loan amount is high and so a large part of the repayment consists of interests. Gradually, the interest payments get smaller, but a larger part consists of the capital repayment. As we lenders get only the capital part, shouldn't we get rising amounts over the loan period? If we get fixed amounts during the loan period, it means that the MFIs are underpaid in the beginning and are subsidizing our lending activity. That is not what we wanted, is it? Or do borrowers by chance make fixed capital and variable interest repayments, which means for them decreasing instalments? I don't believe so. Has anyone spotted a repayment schedule with increasing amounts over the period?
Robert