Loans, Mortgages, and Amortizations

Goal: When our own future is at stake, most of us want to use every effective approach we can find. The mathematical mode of thought is not the only way to approach decisions, but the reasoned strategies that mathematics illustrates are powerful tools that give us surprising strength for analyzing and conquering life's issues.

From The Heart of Mathematics:

      We have been watching money coming in and growing, but in real life we frequently watch money going out and shrinking. Often money happily comes in when we borrow, and sadly goes out when we have to pay back the loan or mortgage. This process is deadly.
      Morticians bury dead people. Mortuaries are where dead people are praised before they are buried. Mortality means death is in our future. There's a pattern here. Mort means death, and words with mort in them are often deadly. Among the deadliest are mortgage and amortize. Mortgage comes from the Latin meaning a "death pledge." To amortize a debt means to "kill the debt."
      To understand loans and mortgages, interest, and payments, we adopt the effective thinking strategy that we have encountered so frequently, namely, we start with simple cases, understand them deeply, and then apply the ideas we have learned to more complicated situations.
Here we apply these methods of thoughts to the decisions we will face in life related to student loans, house and car buying. The events described here all actually happened, and the same language is used to describe them.

When a bank loans money it expects to make back what it would have elsewhere, while we pay back in installments. So we set up lump sum with the principal=loan for the banks earnings, and solve for our monthly payment needed to reach that amount via periodic payment.