Annual Percentage Rate: finally solve the equation thanks to wikipedia

Thanks to Wikipedia, it showed me there is a recursive relation between the consecutive loan payments where P(n) = P(n-1) + P(n-1) * r – c = AmountOwe + Interest – Payment. This is totally different than my assumption that we the principal equally month by month, calculate the interest in that way and evenly distribute them to have a fixed monthly payment. Once we are sure about the equation, it is just a matter of solving the series problem. I am not kidding, this is a problem that could be easily solved by a high school student if you received your education in China. Here is a hand calculation with some math tricks, a bit different from the one in Wikipedia but it works. 🙂

apr_handcalculation

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