Mortgage Alphabet Soup



At one point in my life I made a living by being a teacher. Now, I am constantly on the lookout for actual work situations that can be turned into word problems. Here's a redacted version of something I was doing a not too long ago:

Joe buys a house and takes out a mortgage for X dollars. The loan is at an interest rate of I and for a total term of N months with a level payment each month. However, M months later, Joe sells his house and pays off the loan early, which means that he makes a payment of Y dollars in addition to his normal monthly payment to extinguish his obligations.

Problem: In terms of X, I, M, and Y, provide the closed-form expression for N.

This problem can be solved with nothing more than high-school algebra. I guess the real-life problems I solve at work don't really need much more education than that. It does turn out, however, to be a lot more involved than one might guess.



Last Updated September 2007
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