Mortgage Balance Practice Problem

I have a student who is looking at refinancing her mortgage right now (mortgage interest rates have dropped recently). She is looking to refinance $100,000 mortgage and she is getting mortgage interest rate quotes at 5.5% for a 30-year mortgage with montly payments. As we know, people typically do not stay in the same property for 30 years. She expects to move in 5 years and she would like to know the balance of this loan at the end of 5 years.

What will be the remaining mortgage balance of this mortgage at the end of 5 years?

The easiest way to solve this problem is to use the following rule: The balance of a mortgage at any point in time is just the Present Value of the remaining mortgage payments discount at the mortgage contract rate.

HINT: Step 1 - calculate the mortgage payment. Step 2 - calculate the number of remaining payments. Step 3 - discount the remaining payments back to present value.

Would anyone like to show the answer and step by step calculations? If so, please comment to this post.