In 1996 Peyman Milanfar, a reader of *Mathematics Magazine*, presented a quick way to estimate monthly payments on a loan, passed down from his grandfather, who had been a merchant in 19-century Iran:

The interest is calculated as

The exact formula given in finance textbooks is

where *C* is the monthly payment, *r* is the monthly interest rate (1/12 the annual interest rate), *N* is the total number of months, and *P* is the principal. Rendered in that notation, the folk formula becomes

“In many cases, *C _{f}* is a surprisingly good approximation to

*C*,” particularly when the principal is fixed, the monthly interest rate is sufficiently low, and the total number of months is sufficiently high, Milanfar writes. For example, for a four-year loan of $10,000 at an annual rate of 7% compounded monthly, the precise formula gives a monthly payment of $239.46, while the folk formula gives $237.50.

“While its origins remain a mystery, the method is still in use among merchants all around Iran, and perhaps elsewhere.”

(Peyman Milanfar, “A Persian Folk Method of Figuring Interest,” *Mathematics Magazine* 69:5 [1996], 376.)