I think the interest rates charged by local field partners can seem high at first, but Kiva has a small section on their site in their About -> About Microfinance -> 6. Why are microcredit interest rates so high? section.
Quote:
The nature of microcredit – small loans – is such that interest rates need to be high to return the cost of the loan.
"There are three kinds of costs the MFI has to cover when it makes microloans. The first two, the cost of the money that it lends and the cost of loan defaults, are proportional to the amount lent. For instance, if the cost paid by the MFI for the money it lends is 10%, and it experiences defaults of 1% of the amount lent, then these two costs will total $11 for a loan of $100, and $55 for a loan of $500. An interest rate of 11% of the loan amount thus covers both these costs for either loan.
The third type of cost, transaction costs, is not proportional to the amount lent. The transaction cost of the $500 loan is not much different from the transaction cost of the $100 loan. Both loans require roughly the same amount of staff time for meeting with the borrower to appraise the loan, processing the loan disbursement and repayments, and follow-up monitoring. Suppose that the transaction cost is $25 per loan and that the loans are for one year. To break even on the $500 loan, the MFI would need to collect interest of $50 + 5 + $25 = $80, which represents an annual interest rate of 16%. To break even on the $100 loan, the MFI would need to collect interest of $10 + 1 + $25 = $36, which is an interest rate of 36%. At first glance, a rate this high looks abusive to many people, especially when the clients are poor. But in fact, this interest rate simply reflects the basic reality that when loan sizes get very small, transaction costs loom larger because these costs can't be cut below certain minimums."
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There's more information on it at the CGAP site (linked to on the Kiva page above).
Essentially, if field partners are to sustain themselves financially, they're required to charge interest rates that cover their costs. Some microfinance institutions do prioritise lending at lower rates to be more affordable for their borrowers, but they accordingly have to rely on support from donations to remain financially viable.
Microfinance isn't ever going to be a magic bullet to totally eliminate poverty, but I do think it's had a lot of success in raising millions of peoples' living standards, and that the relatively high interest rates haven't generally stood in the way of that happening.