Though average mortgage rates have dropped to extreme lows never seen before, if you're buying a home or refinancing you can't assume that a lender will always offer you a deeply discounted rate.

When you don't comparison-shop for your loan, you can pay way too much in interest costs, up to nearly $52,000 more than you should over the life of a 30-year mortgage, according to a new analysis from LendingTree.

That's because different lenders can offer rates that vary by 1 full percentage point or more, the study says.

A lower mortgage APR can save you tens of thousands

LendingTree looked at mortgage APRs, or annual percentage rates, which are higher than the standard interest rates you're accustomed to seeing. The popular survey from mortgage company Freddie Mac says the interest on 30-year fixed-rate mortgages this week is averaging a record-low 3.15%.

An APR takes the interest rate and rolls in closing costs, the fees known as "discount points" and other borrower charges, to give a broader picture of the annual cost of the loan.

LendingTree says its research, using data from April, finds the average APRs offered to homebuyers with the best credit scores — 760 or higher — ranged from 3.47% to as high as 4.32% for 30-year mortgages in the amount of $250,000.

Someone with stellar credit who grabbed a high rate without shopping around to find a low one would pay almost $44,000 in extra interest over the 30-year span of the loan, the study says.

Going down the credit score ladder, LendingTree found that:

• The average APRs offered to buyers with credit scores between 720 and 759 ranged from 3.46% to 4.43% — a difference of almost 1 full percentage point. The rate at the low end would save a borrower a little over $50,000 in lifetime interest, compared to the highest one.

• The average APRs offered to buyers with credit scores between 680 and 719 ranged from 3.62% to 4.61%. Scoring a low rate would mean lifetime interest savings of nearly $52,000.

• The average APRs offered to buyers with credit scores between 640 and 679 ranged from 3.87% to 4.79%. The lowest rate would mean lifetime interest savings of almost $49,000.

• The average APRs offered to buyers with credit scores below 640 ranged from 3.69% to 4.16%. The lowest rate would bring lifetime interest savings of about $24,000.

Don't know your credit score? It's easy to take a look for free.

The lesson is to shop, shop, shop around

LendingTree also found big spreads on the rates on refinance loans offered to homeowners.

For example, an owner refinancing into a 20-year loan for $200,000 and having a credit score between 640 and 679 was offered average rates ranging from 3.58% to 4.69% — a difference of over 1 full percentage point.

The lowest rate would save a borrower more than $28,000 over the life of the loan, versus the highest one, according to the LendingTree study.

Lots of people incorrectly think lenders all follow some kind of rule that says a particular person should be charged a particular rate, but that's just not the case, says LendingTree senior research analyst Kali McFadden.

"Lenders do follow an underwriting schema, but they also have a variety of reasons why they might make different offers to the same borrower, and it's an absolute shame to pay so much more for something than you have to," McFadden says.

The lesson couldn't be any clearer: You've got to shop around and compare rates from several lenders, not grab the first loan you're offered. By sniffing out the best rate that's available to you, you can cut down your mortgage payment and save big over time.

"Just think of what even saving $20 a month could do for someone's retirement nest egg," says McFadden.