My Math Forum % payment loan

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 May 26th, 2013, 10:25 PM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,909 Thanks: 716 % payment loan Hope you have fun with this Code: MONTH PAYMENT INTEREST BALANCE 0 1,300.00 1 -130.00 13.00 1,183.00 2 -118.30 11.83 1,076.53 3 -107.653 10.7653 979.6423 ======= 35.5953 Above is a $1300 loan at interest of 1% per month, and monthly payments of 10% of balance, with minimum payment =$100. Since 4th payment using 10% of balance = ~$97.96, then this payment will not be made, but instead the minimum payment will take effect. So, at end of month preceeding month of 1st minimum payment, interest of ~$35.60 has been paid. So in this example, we have: a = amount of loan (1300) m = minimum payment (100) j = percentage of balance (.10) i = interest per month (.01) k = interest paid up to month of 1st min. pay't (?) As a general case formula, k (in terms of a,m,j,i) = ?
 June 5th, 2013, 10:45 AM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,909 Thanks: 716 Re: % payment loan Looks like this wasn't too popular!! u = m / (aj) v = 1 - j + i n = CEILING[LOG(u) / LOG(v)] f = av^n k = i(a - f) / (j - i) ........................................... u = 100 / (1300*.1) = .76923.... v = 1 - .10 + .01 = .91 n = CEILING[LOG(.76923...) / LOG(.91)] = 3 f = 1300 * .91^3 = 979.6423 k = .01(1300 - 979.6423) / (.10 - .01) = 35.5953

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