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There's a reason so many homeowners rushed to refinance in 2020. Mortgage refinance rates have been extremely competitive, helping those homeowners reap a world of savings. 

If you missed the boat on refinancing in 2020, or it didn't make sense for you -- say, you needed time to boost your credit score -- then worry not. There's a good chance refinance rates will remain low throughout 2021, so you still have plenty of opportunity to save money in paying off your home. And if you're eager to refinance, here are three strategies to look at. 

1. Refinance to a loan with the same term

Many people who refinance simply get a new mortgage with the same term as their existing mortgage. And that's a route you can consider. In other words, if you have a 30-year mortgage, you could refinance to a new 30-year mortgage -- but at a lower rate. 

There's certainly nothing wrong with refinancing to the same loan term, but you should know that this may not be the best idea if you're already several years into paying off your mortgage. Imagine you took out a 30-year mortgage six years ago. If you refinance to a new 30-year loan, you'll reset the clock on your mortgage and end up paying it off over a longer total time. On the other hand, if you're only a year or two into a 30-year mortgage, resetting the clock isn't so terrible. 

You may, in some cases, find a mortgage lender willing to do a custom refinance term. When you apply for a mortgage, you're usually limited to a 15-, 20-, or 30-year loan, though some lenders offer a 10-year mortgage as well. But there are lenders that will give you, say, a 24-year mortgage if that's the number of years left on your loan. It pays to explore your options. 

2. Do a cash-out refinance to pay off other debt

With a cash-out refinance, you borrow more than your remaining mortgage balance and get a check for the difference. That extra money is yours to spend as you please. If you're carrying costly debt (say, a few credit card balances at an average interest rate of 20%), a cash-out refinance could make a lot of sense for you with today's low rates. 

Imagine you owe $150,000 on your mortgage and $20,000 on credit cards that are charging you 20% interest. With a cash-out refinance, you'd borrow $170,000, use $150,000 to pay off your initial mortgage, and then use $20,000 to pay off your credit cards. You'd then repay that entire $170,000 as a single loan. And if you score a 3% interest rate on your cash-out refinance, it means you'd effectively pay that $20,000 in credit card debt at a rate of 3%, not 20%. 

3. Switch from a 30-year loan to a 15-year loan to pay off your home sooner 

Many homeowners opt for a 30-year mortgage over a 15-year loan because that results in lower monthly payments. But with a 15-year mortgage, you're apt to score a lower interest rate than with a 30-year loan. So if you're going to refinance, at today's rates, a 15-year loan could end up being far more affordable than you'd think. If you can swing the higher monthly payment, it could make a lot of sense. That way, you'll save money on interest and pay off your home much sooner.

This move especially makes sense if you bought a home a bit later in life and are eager to pay it off by the time you retire. Say you're 50 years old, with 26 years left on your 30-year mortgage. If you refinance to a 15-year loan and stick to that payment schedule, you'll be mortgage-free by age 65, a common time to retire or at least start thinking about it. 

If you're interested in refinancing your mortgage next year, think about which strategy makes the most sense for you. With the right approach, you could come away with a lot of savings.