EXAMPLE 8 Home Equity

My wife’s parents sold their house in rural Minnesota to move to the town where we live. They had bought their house in 1980 with a 30-year mortgage for $100,000 at an 8% interest rate. After 22 years, how much equity did they have in the house—that is, how much of the principal had been repaid? And how much did they still owe on the house?

What may shock you (and disappointed them) is that when they sold their house in May 2002—after 269 months of payments, almost exactly three-quarters of the 30 years of the mortgage—they had only $50,000 in equity (hence, they still owed $50,000 on the house) but had already paid $147,000 in interest. Three-quarters of their payments had gone to interest.

We can use the amortization payment formula to determine just how much equity they had after 269 months of payments, but first we need to Í determine their monthly payment. We see , months, and monthly interest, getting .

Now we use the formula again, this time “in reverse.” Knowing and , we find out how much of the loan would have been paid off by the remaining payments of $733.76:

This is how much my parents-in-law had yet to pay, so their equity was . (The above formula would not apply if they had made larger or additional payments.)