OK, This Time I've Really Got It: Grameen's Interest Rate Revisited

[Note: This post may be wrong!]In September, I determined that the effective annual interest rate on the Grameen Bank's standard loan product is exactly 23.3250889% (after factoring in share purchases and dividends). I know, you were thinking it was more like 23.3250888%.Well, it turns out we were both wrong. It's actually 16.7831509%. Or thereabouts. I had neglected to consider Grameen's pioneering "top-up" mechanism, which allows people to borrow back the full loan amount after 6 months or more of steady repayment. On a standard one-year loan, clients can reborrow at a time of their choosing between 26 and 52 weeks. They cannot, however, take a larger loan until they have fully repaid the current one. Here's a fine story of the flexibility of the top-up loan in Portfolios of the Poor---somewhat off the topic of the interest rate, but worth reading:What is the connection to the interest rate? When Ramna repeatedly reborrows without fully repaying, she is raising the average balance of her loan without raising the cost. Her weekly payments are the same as they would be for an un-top-uppable loan of the same amount. Since the balance goes up but the interest doesn't, her effective interest rate goes down! In fact, her interest rate depends on the timing of her top-ups. So in suggesting a rate of 16.78% above, I was being even more a facetious than it appeared.In my revised Grameen interest rate Excel file, I added a sheet to simulate a top-up scenario inspired by Ramna. A borrower takes a 5000 taka loan with a nominal one-year repayment schedule and then tops up every three quarters like clockwork for 10 years. That yields a rate of 16.78% with compounding. More rapid topping up would generate a lower rate. No topping up would produce a rate more like the 23.33% I calculated before. Interestingly, these numbers bracket the Grameen Bank's reported gross portfolio yield of 19.58% for 2009, which is the ratio of interest received to average loans outstanding, a rough proxy for the interest rate. In other words, topping up helps explain why my previous estimate of the interest rate, like most others, markedly exceeds the gross portfolio yield.In sum, it appears that the topping up mechanism in Grameen II not only made its loans more flexible but lowered the effective interest rate in a way that had not been understood.