The Mathematics of Refinancing

Financing describes a method of raising funds or capital. Many people finance an asset and pay for it in installments, as opposed to paying a sum up front. The cost of financing is the interest expense imposed by banks. This cost motivates people to search for the lowest interest rate possible. Even after a loan is taken, people look towards refinancing in order to achieve an even lower interest rate.

We model the effects of refinancing loans at lower interest rates. Mathematically, we show how the timing for refinancing that is most beneficial to the borrower depends on the terms left on the loan and the refinancing fees that could be imposed. Also, we look at how the refinanced loan is to be structured. We examine examples from the two most common financing types in the U.S., automobile and real estate loans. For instance, should the borrower always refinance if there is a lower interest rate? Can various fees make refinancing at lower interest rate worse than the original loan? This article will help to arrive at the answers to these questions.