I'm trying to create and then solve A D.E. that deals with mortgage amortization and mortgage prepayments. By playing around with the prepayment option on mortgage amortization calculator at http://mortgage-x.com/calculators/extra_payment_calculator.asp , I found that the ratio of money saved at the end of the loan vs principal prepayment differed depending on the date you made the prepayment (of course), and the prepayment amount. The ratio of the prepayment amount vs money saved wasn't the same for all prepayment amounts. So there is an unknown, optimal, highest value prepayment amount that saves you the most money per dollar spent. To put is simply, a $100 prepayment can save you $500 (due to the nature of compound interest). I want to set up and solve a diffEq such that I'm left with a 3-dimensional function where x is the month number (of the life of the loan) that the prepayment is made, and y is the pre-payment amount. z-axis would represent the amount of interest saved at the end of the mortgage loan. Is that way too hard to figure out or what? All I've been able to do is just get points for the function but I don't know how to set the diffEq up.