Something I've been fuzzy on is what interest rate the Grameen Bank charges. Seems like the sort of thing an aspiring microfinance expert should know.

Fortunately, the Grameen Bank is the world's best-documented microcreditor. One can, for example, quickly learn from the Bank's website that the rate is 16 percent.

...except that another page on the site says the rate is 10% on a "flat" basis, which means that when someone borrows 1000 *taka* and repays in weekly installments over the course of year, she pays 100 *taka* total in interest. Since she pays that 100 *taka* on a average balance of 500 (the balance falls steadily from 1000 to 0 over the year), her effective interest rate is more like 100/500 = 20%. That's twice the flat rate, as the Grameen site makes clear.

So: 20%.

This lines up pretty well with MixMarket's numbers on Grameen's gross portfolio yield, which is the ratio between interest received and loans outstanding. They have the GPY coasting from 22.4% in 2005 to 19.6% in 2009.

Ah, Microfinance Transparency would remind us, but the true cost of credit includes more than the interest rate. Clients may be required to put some of their borrowings into creditor-run savings accounts as a kind of collateral---"forced savings"---which reduces available credit without proportionally reducing interest payments and thus effectively raises the rate. There may be up-front fees too. In the case of Grameen, each member must buy a 100 *taka* share of the Bank once her forced savings balance is high enough to pay for it.

And the complications have complications. True, a Grameen member can't get that 100 *taka* back until she quits the bank, but in recent years Grameen has paid handsome dividends on those shares---for instance, 100% of face value for 2006, 30% for 2009.

And is forcing people to save purely a cost? One reason people borrow is that it disciplines them into regularly setting aside small amounts in order to make big purchases. Forced savings does that too. If people keep borrowing and repaying, all the while building up their forced savings accounts, then their net debt may fall and so will the associated stress.

Another complication: today, Grameen clients must save into two different accounts, with different rules. 2.5% of each new loan, and additional savings each week, go into the Personal Account---from which the money may immediately be withdrawn. Another 2.5% goes into the Special Account, to which access has historically been much more limited. Asif Dowla, Grameen's first accountant, says that the rules were recently changed to free up access to even the Special Account. On the other hand, I'm told that Grameen officers often exercise discretion over the interpretation and implementation of rules (Grameen clients have little access to the documents stating their rights). And those officers have a strong incentive to limit access to savings because it is their insurance against missed payments. They can dip into the savings to keep their branch's payment record clean. So it does not seem safe to assume that Grameen members can easily access all their savings.

So it turns out that computing the interest rate is a complex business. Not only are there several factors to consider, but the impact of some of them depends on a borrower's loan history. For instance, that one-time 100 *taka* stock purchase matters much less to someone who routinely borrows 10,000 *taka*/year than someone who stays at 2,000. In fact, if the latter someone is forced to save 10% of her loan each year, then after nine years, she'll be borrowing 2,000 while holding savings of 1,800, for a net loan of just 200. If she pays 20% interest on each gross borrowing of 2,000, that works out to *200%* interest on her *net* borrowing! A cycle later, her net credit goes to zero, and her interest rate is infinite--which calls this whole framework, viewing forced savings as a pure cost, into question.

This is how, roughly speaking, Karl Borden of the University of Nebraska constructed a scenario in which the Grameen Bank's effective interest rate is 556.4% per year for ten years. (Borden also jacks up the rate, I believe, by mistakenly treating all forced savings as forever lost to the client, rather than simulating the eventual return of such savings to the savers.) That rate is mathematically equivalent to turning a seven-dollar debt into a billion-dollar one in 10 years. Those borrowers better be careful!

In a more realistic scenario, in which a client borrows and repays 2,000 the first year, 3,000 the next, 4,000 after that, etc.---but still treating savings as if it goes into a black hole---Borden gets an average rate of 44.1%.

In order to get to the bottom of this question, and inspired by a fantastic, general-purpose rate-calculating spreadsheet from Microfinance Transparency, I decided to build a custom spreadsheet for Grameen. Unlike the general tool, it accounts for the fact that Grameen pays on interest on savings (8.5%/year). It represents the repayment schedule a bit more precisely. (Standard one-year loans are repaid over 52 weeks, of which 6 are holiday grace periods; the first 45 of the 46 payments are 22 *taka* of principal repayment and 2 of interest per 1000 borrowed; the last is 10 each of principal and interest.) The spreadsheet also facilitates simulation of various 10-year scenarios. And it performs a proper internal-rate-of-return calculation, if you know what that means, to fully account for the compounding of interest.

In the default scenario, the borrower takes loans of 1,000, 2,000, ... up to 10,000 over 10 years. I treat only the 2.5% of loans going into the Special savings account as inaccessible. I ignore the other forced savings on the idea that they are immediately accessible, so that a borrower can if she wants take the money right back out and add it to her borrowed funds. At the end of the 10 years, the borrower repays her last loan, takes out her accumulated Special savings (including interest), and leaves the Bank. I ignore the need to purchase the 100 *taka* share because of the wide uncertainty about Grameen's future dividend payments. [But see update at end.]

My bottom line? 24.28%/year. But if I change the fraction of loans that borrowers are compelled to save from 2.5% to 5% (maybe some Grameen officers routinely block access to most savings), the credit interest rate rises to 28.75%. You can load the spreadsheet and change the parameters near the top in columns B and E, then view the resulting interest rate in cell H2.

Two last notes:

First, Borden did something else, quite special: he obtained weekly transaction data for all 43 borrowers in a Grameen "center" (borrowing group) in Rajbari District over eight years and used this to compute effective interest rates actually paid. Using a consistent (but flawed) methodology this lowered the rate from 44.1% to 35.6%. So it seems that deferred and missed payments are common enough to lower the effective interest rate substantially. The same should apply to my methodology: even for clients for whom my 24.28% is number is perfectly correct in theory may pay less in practice. On the other hand, clients who save money this way may pay with higher stress.

Second, inflation matters. 24.28% is a great deal if inflation is 24%---for then the *real* interest rate is just 0.28%. In fact, inflation in Bangladesh has run higher than in most rich countries, so what "feels" like 24.28% to a Bangladeshi would be more like 20.28% for an American:

On balance, Grameen Bank loans, like most microcredit in South Asia, seem pretty cheap.

On whether Grameen Bank clients are properly informed that what is billed as "10%" works out to more like 24%, see last year's Reflections on Transparency.

Update: In response to Fehmeen's suggestion, I have incorporated the mandatory share purchase and the dividends into the spreadsheet. To keep it consistent with the results I quote above, I have added a parameter to turn off this consideration. Change "Factor in share purchase?" in the upper left from 0 to 1 to enable it. Using a dividend rate of 30 *taka*/share (the rate of the last two years) lowers the nominal credit interest rate from 24.28% to 23.33%. Keep in mind, however, that with the Grameen Bank, as with any investment, risk and return ought to go together. The spreadsheet assumes, probably incorrectly, that dividends will be paid at the same rate each year like clockwork. It therefore reflects the high recent returns to ownership of Grameen shares, but not the associated risk.