Larry Swedroe posted an **interesting article** on how to do the math on a mortgage refinancing to find out whether or not it’s to your benefit to refinance. He used the following example:

• 12 years left on a 15-year mortgage.

• Current mortgage rate is 4.75%.

• Current monthly payment $1,369

• Current balance on the mortgage around $150,000 (this is the amount to be refinanced).

This couple is looking to refinance into:

• 15-year mortgage.

• $150,000 loan.

• $3,000 in closing costs (to be paid upfront).

This couple is in the 25% income tax bracket.

So…based on those numbers, would it be a good idea to refinance?

Well, as Larry points out, there are a lot of things to consider before jumping into a refinance.

1. In this example, the spread between the two interest rates is less than a 100 basis points (less than one percent). Naturally, the bigger the spread, the more advantageous it is to refinance.

2. There is more to the calculation than simply looking at the difference in payments since the payment includes principal, which is your own money. So, we have to look at the difference in the interest portion of the payment.

3. As Larry also points out, interest payments are tax deductible (if you itemize your deductions). Larry uses the 25% income tax bracket for his example. Based on that, the couple is paying $.75 for each $1.00 of interest. Basically, what this means is that this makes the refinance less advantageous (you’ll see this in the spreadsheet).

4. This couple is already three years into their loan. They are looking to refnance into a new 15-year mortgage. That means they have paid 3 years of interest on the old loan and will be paying 15 years of interest on the new loan for a total of 18 years of interest.

5. The closing costs are paid upfront.

After running the example, I came to the conclusion that refinancing this loan will cost an additional $702 in after-tax interest. I arrived at this number by adding up the three year’s of interest paid on the original loan plus the 15 year’s of interest on the new loan. Were they to continue with the old loan, they would have paid a total of $70,417 in interest ($52,812 after-tax in a 25% income tax bracket).

What Larry leaves out, in my opinion, is a discussion of the opportunity cost between the two loans. By choosing to refinance, this couple would be freeing up cashflow that could be put to work elsewhere (unless they are using the cashflow to shore up their budget). The payment difference of $296 per month could be invested elsewhere for the next 12 years. Using a monthly total return on the S&P 500 Index of .75% (including a management fee), that $296 per month payment difference could grow to more than $112,000 in 15 years. If they invested the $3,000 plus the entire $1,369 monthly payment for 3 years after the end of the original mortgage, they would have over $60,000 at the end of 15 years. Another thing worth mentioning is that all of the $296 per month could be put into a Roth IRA where only a portion of the $1,369 payments could be put in a Roth because they would exceed the Roth limits.

Based on those numbers, the refinance looks like a no-brainer. But, I left out three things: 1. Investing in the stock market is not a sure thing and 2. I didn’t make adjustments for taxes, which favored the refinance. 3. In order for the scenario to work, the payment difference MUST be invested and not spent.

With that said, I am making available the spreadsheet I used for this post, which you can download here: **Mortgage Amortization Comparison (Two 15-year Mortgages)**. I didn’t spend a lot of time making it user-friendly but if you understand the basics of Excel, you can get in there and change up the variables yourself.