For some homeowners, today's historically low interest rates have created much needed breathing room for overstretched budgets. But if you're fortunate enough to already have a little extra space in your monthly budget, refinancing with a 15-year mortgage instead of a 30-year mortgage can help you tap into even more significant savings.

Two general rules of thumb when refinancing involve keeping your home long enough to recoup the upfront closing costs, and trying match the term of your new loan to the remaining years on your existing loan. While it's always important to make sure refinancing actually saves you money, you have more flexibility when choosing the term on your new loan. This is particularly true if you're thinking of choosing a shorter term.

For example, say you have 25 years left on a $200,000 30-year fixed-rate mortgage (FRM) with an interest rate of 7.0%. You have a choice between refinancing with a 30-year loan at the national average rate of 5.42% or a 15-year loan at the average rate of 5.02%; both averages are from BankingMyWay.com's Mortgage Rate Index. Let's assume refinancing with either loan will cost $2,500 at closing.

In this case, refinancing with the 15-year loan will cost you an extra $160 per month, instead of saving $271 per month with the 30-year refinance. However, the 15-year loan will save you a whopping $130,846 in interest payments -- $113,000 more than the 30-year loan. (See the table below for a comparison.)

Remaining 25-yrs
Interest rate: 7.0%
Monthly Payment: $1,331
Total Interest Payment: $210,916

30-Year Refinance
Interest rate: 5.42%
Monthly Payment: $1,060
Total Interest Payment: $193,160

15-Year Refinance
Interest rate: 5.02%
Monthly Payment: $1,491
Total Interest Payment: $80,070

The six-figure savings in interest payments on the 15-year loan is because more of your monthly payments go towards paying down the principal of your loan. With the 15-year loan, $8,635 (48%) of the $17,892 in payments the first year goes towards your principal. By comparison, only $2,574 (20%) of your first year's payments of $12,715 goes towards principal with a 30-year loan.