Q: Ilyce, my wife and I have a great house in a great neighborhood in Atlanta. It is worth in excess of $400,000.

We owe $130,000 on the first mortgage, which is a 15-year fixed-rate loan at 4.875 percent. We have a home equity line of credit (HELOC) with a balance of $13,000. That loan is at an adjustable rate mortgage (ARM) that is currently fixed at 2 percent.

We’ve decided to aggressively pay off both loans in the next 3 years. The question is, should we refinance both loans into one 15-year fixed-rate mortgage at a lower rate or use the home equity line of credit to pay off the first loan, and then pay that loan off at the much lower rate.

A: Don’t refinance. If your goal is to eliminate your debt load over the next three years, you won’t get much benefit out of the lower interest rate. Some refinances cost homeowners two to five thousand dollars.

I really don’t think you’ll get your money out of it. Instead, put all that extra cash you’d shell out for closing costs toward paying off your home mortgage, and then your home equity line of credit.

Why pay off your primary mortgage first? Well, with interest rates as low as they are today and with rates likely staying low for a while, you’ll benefit from the reduction in your loan balance on your first mortgage. If you’ve had your 15-year mortgage for some time, your payment will go towards paying principal down and shortening the life of your loan considerably.

Your equity line of credit is rather low and you’ll be able to pay off that loan amount in a rather short amount of time, so you might as well enjoy the extraordinary low interest rate that loan carries now, while you have it.

If you were to use your equity line to pay off your primary loan, the risk you’d take is that the interest rate home equity line of credit could jump up immediately as interest rates rise. So you’d be hedging yourself by paying down your primary mortgage and keeping some of your equity line.

While a 15-year loan at 4.875 seems “high” compared to the 4.1 percent some folks are scoring on 15-year loans at the moment, it’s an excellent long-term rate and you might not break even for several years given how little you will save and how much you’ll pay to close if you decide to refinance now.

If you found a lender that was willing to refinance your 15-year loan without any points and fees, then you’d save immediately on your monthly payment. However, if you look at the difference in your monthly payment between what you are currently paying monthly and what you would pay on your new loan, you might think that the difference is your savings. But when you refinance, you extend the length of your loan.

To actually compare your current loan with what you would receive on a new fifteen year loan, you need to compare both loans with the same end date. If you are five years into your 15-year mortgage, you’d need to compare that mortgage with a new 15-year mortgage but change the maturity date to ten years to actually see your monthly savings. At that point you’ll realize that the monthly savings are pretty small on your loan balance.

Remember, when you have a 15-year loan, you’re already paying a substantial amount toward the principal of the loan each month. Making an extra payment a year might only shave off a year or two of payments – still a substantial sum, but not nearly the bang for your buck that you get with a 30-year loan. That’s because you’ve already saved those 15 years of interest and are now working on shaving another 5 years.

I ran the numbers on a $200,000 15-year loan at 4.875. The monthly payment is $1,569. Every extra annual payment of $1,569 will shave another year off the loan. So, if you make one extra payment per year, you’ll cut your loan term to 14 years. If you make two payments, you’ll pay off the loan in 13 years, and so on.

If you make a $1,569 extra payment each month, or 12 extra payments per year, you’ll pay off the loan in 7 years, and only pay $31,000 in interest.

In your case, you want to pay off both loans in three years. If you can find about $160,000 in cash to do that, then you’ll be able to achieve that goal.

There are a bunch of calculators online that will help you make the calculations. I used the amortization calculator at eloan.com, but there’s also a good calculator at ThinkGlink.com and on many other sites.