Shutterstock

Compound interest, Albert Einstein apocryphally observed, is the most powerful force in the universe. Whether he actually said this, it's certainly true that interest payments consume an enormous amount of the average American's budget.

Homeowners feel this pinch with every payment they make. At time of writing the average interest rate on a 30-year mortgage was 4.23%, with an average mortgage costing a little over $200,000. Even though 4.23% might not sound like a lot, over three decades it adds up to more than $153,000 in interest payments alone.

You read that right. The average homeowner will pay almost as much in interest as the entire house is worth. (Of course, city dwellers might have to dig deep to sympathize. That average homeowner will pay $926 per month for their freestanding home, less than half what many people pay to rent a one-bedroom urban apartment.)

Which is why refinancing matters. Shaving even half a point off your interest payments can save you tens of thousands of dollars in the long run. Here's what you need to know.

When Should You Refinance Your Mortgage?

First things first, when and why should you refinance?

Boiled down, refinancing is when you take out a new loan to pay a previous loan. For example, say you owe $200,000 on your mortgage. To refinance you would take out another $200,000 loan from a different lender, use that to pay the first loan off, then resume making payments to the new lender.

The goal of refinancing is to secure better terms for the loan. Typically this means reducing your interest rate, which over the lifetime of a home loan can mean serious money. Just be careful that all the terms of your new loan are favorable. In particular, since you are taking out a new mortgage it's possible that the lender will want to reset the payment schedule, giving you a new 30-year payment plan. Depending on how long you've already spent paying for your house, this can keep you in debt for many more years to come and can potentially increase the total amount of interest you end up paying.

The best reason to refinance your mortgage is if you think that you can get better terms on this new loan than on your original one. For example, if your credit score has significantly improved or your financial position is much stronger than when you originally bought the house, this might be an excellent time to refinance. In both of these cases a lender might well extend better terms than you got the first time around.

You might also consider refinancing if your property value has substantially improved over time. For example, say that in the past 10 years your neighborhood has become the hot place to live. Your loan is now secured by a house worth far more than at the time you bought it. A new lender might well give you far more favorable terms on a loan secured by this newly-more-valuable property.

How to Refinance a Mortgage

Refinancing is both straightforward and complicated at the same time. The process of finding and comparing offers is, ultimately, not difficult. Figuring out if those offers are right for you… that's trickier.

If you've decided that now is the right time to shop for a refinanced mortgage, it's best to begin with the following steps:

Set Your Goals

What do you want to get out of your refinance? Would you like to reduce your interest rate, lower your monthly payment, change the number of years left on the mortgage or some other goal entirely? Pull up a mortgage calculator to figure out the different moving pieces on your payment plan and decide what you would like to achieve and how it would fit into your personal budget.

Understand Your Current Mortgage 

Review the terms of your current mortgage. Many home loans have fees and penalties attached to paying them off early; the lender wants to make up for all the interest you won't pay them. Understand how much money (if any) you'll owe for paying off your original mortgage, since this will change the math on how much refinancing saves you.

Shop for Rates and Get Preapproval 

Now it's time to actually start looking for a refinancing. Begin with your bank and any other financial institution you have a relationship with. Then go online and look for refinancing options, such as with Quicken or Bank of America (BAC - Get Report) (two of the more highly recommended options, according to a survey conducted by U.S. News).

Fill out the paperwork to get prequalification and preapproval from any lender that interests you based on their advertised rates. This is an important part of the process because it will tell you how much the lender can actually offer you and at what terms. Until you have preapproval, you don't specifically know what your refinancing will look like. Do this within a short period of time, preferably less than 10 business days for all of the preapproval applications, otherwise it might negatively impact your credit score.

Compare Costs

Return to your mortgage calculator tool linked above. Use that to determine how much money you'll save under these new terms, then compare that with your total costs (more about that below). Make sure that once all is said and done, you'll actually save money.

Gather Your Documents

Once you actually apply for this loan you'll need a substantial number of documents to prove your identity and financial situation. These typically include: Recent tax returns; W-2 or 1099s from at least one, preferably two, years; recent pay stubs; recent bank statements; an accounting of all current debts; proof of payment on your current mortgage.

Application and Appraisal 

When you have selected a lender and gathered your documents, fill out the application for the loan. As part of this process the lender may (and likely will) have the property appraised. Refinancing lenders apply what is called the Loan To Value limit (LTV). This is how much of the property's value they're willing to lend you. For example, say your refinancing offer has an LTV of 60% and your property is worth $100,000. The lender could offer you up to $60,000.

The appraisal will determine whether the lender can offer you a loan large enough to pay off your existing mortgage.

Close on the refinance

If your LTV allows for a large enough loan and the terms are favorable, accept the offer and close on the refinancing.

How Much Does It Cost to Refinance a Mortgage? 

Refinancing can come with a lot of unexpected costs. In addition to any early payment fees attached to your original mortgage, you should expect some or all of the following costs to apply:

• Appraisal and inspection fees, which can include not only the professional property appraisal but also inspections for insects, flood danger and mold.

• Loan application fees charged by the lender for reviewing your application.

• Origination fee for creating a new mortgage.

• Attorney's fees if you require the help of a lawyer (either for practical reasons or, in some state, by law).

• Title and recording fees for ensuring that you are, in fact, the proper owner of this home.

• Credit report fee for processing the credit check as part of your application.

• Transfer taxes charged by local governments to record a property transaction.

• Insurance payments if the refinance requires any changes to your property or mortgage insurance.

• Up-front payments, typically as either an initial payment on the interest or an initial payment in exchange for a lower interest rate.

What Are the Pros and Cons of Refinancing a Mortgage?

Under the right circumstances refinancing can save you a substantial amount of money. Some of the biggest reasons to do it include:

Converting Your Interest Rate

If you have an adjustable rate mortgage and the interest has gone up, you might want to convert to a fixed rate in order to get that under control. By contrast, if the market looks favorable or if you plan to sell within a few years, you may want to switch your fixed rate mortgage to an adjustable one.

Reducing Your Interest Rate

Taking 1 - 2 points off of your interest rate will usually make the costs and hassle of refinancing worthwhile. If your situation has changed and these days you can get a much better interest rate than when you first bought in, you may well save a lot of money.

Reducing the Term of the Loan

Thirty years is a long time to pay a mortgage. If you can afford to accelerate payments, refinancing can let you turn that into a substantially shorter payment plan. This, in turn, will result in you paying far less in interest than you would have otherwise.

Making Home Improvements

If your property is now worth more than the remaining mortgage you can use what's called a "cash-out loan." This is a refinancing option where you get more than the balance is worth. For example, say you have a home worth $150,000 and only owe $100,000 on it. If a lender gave you the full value of the property in a mortgage, you would end up with an extra $50,000 in cash.

You can use that to make home improvements, expanding and building on the house to increase its value. This is a particularly good idea if you plan to sell in the near future and won't be carrying that extra debt for long.

But refinancing has its dark side too. Some of the biggest reasons not to do it include:

Taking Cash-Out Loans

A cash out loan can create value if used the right way. But don't forget that this is a loan and the juice, as they say, is running. Unless you use this money very carefully, you might find that it was just a very expensive way of getting a short-term loan.

Increasing Your Loan Term

Many lenders will offer you a brand-new 30-year mortgage when you refinance. This isn't always in your best interest. While this will give you the lowest monthly payment, it also means effectively starting over on paying your mortgage. If you bought the house recently it's no big deal, but what if you bought your home 12 years ago? On a new 30-year note you'll end up paying for this house for 42 years.

That's a long time and a lot of interest.

The Costs Outweigh the Benefits

Refinancing can come with a lot of hidden costs. Before you pull the trigger, make absolutely certain that you understand all of them and have done the math carefully. Otherwise you might find yourself spending $21,000 to save $20,000.

It's never too late - or too early - to plan and invest for the retirement you deserve. Get more information and a free trial subscription to TheStreet's Retirement Daily to learn more about saving for and living in retirement. Got questions about money, retirement and/or investments? We've got answers.