in an effort to get the prize, im just going to post this and hope it's right

calculate a loan payment or amortization schedule manually if you like running the numbers yourself or want to verify the accuracy of an online loan calculator.

The formula is M = P * ( J / (1 - (1 + J)^ -N)).
M: monthly payment
P: principal or amount of loan
J: monthly interest; annual interest divided by 100, then divided by 12.
N: number of months of amortization, determined by length in years of loan.

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Follow the following steps:
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Calculate 1+J. M = P * ( J / (1 - (1 + J)^ -N))
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Take that to minus N power. M = P * ( J / (1 - (1 + J)^ -N))
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Subtract answer from 1. M = P * ( J / (1 - (1 + J)^ -N))
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Divide the monthly interest (J) by this number. M = P * ( J / (1 - (1 + J)^ -N))
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Multiply the result by the principal or amount of loan. P * ( J / (1 - (1 + J)^ -N))