February 05, 2004
Intertemporal Substitutiion
Why do people save money?
We begin this discussion with a review of intertemporal substitution. This extension of the two goods - two prices diagram shows how a utility maximizing agent chooses his or her optimal consumption in two time periods given the ability to save and borrow money at interest rate R.
When we incorporated inflation into the analysis, we found that using the real interest rate instead of the nominal interest rate allowed us to analyze the problem with minimal changes to the setup.
Mortgage Refinancing
The option to pay off a mortgage early allows homeowners to save money when interest rates decrease, but it introduces a risk for investors in mortgages.
We calculated the new payment amount when a 10% mortgage is ten years old, the mortgage rate is down to 6%, and the homeowner refinances. The balance due is the present value of the remaining payments at the original interest rate. The mortgage would have been worth $121,696 if only the owner could never refinance.
