# Mortgage Borrowers Thinking About Paying Down Their Loan Balance Should Know How Mortgage Amortization Works

Feb 26, 2015 | **Updated** Apr 28, 2015

Jack M. Guttentag Professor of Finance Emeritus at the Wharton School of the University of Pennsylvania

Recently, I have been getting a lot of mail from mortgage borrowers asking about amortization. Most are considering whether to pay down their loan balance more rapidly, and have suddenly realized that they don't know how best to do that, or even whether it is a good idea because they never fully grasped how mortgage amortization works.

This article explains the essentials of amortization, and why in today's market it is a good idea for most borrowers to speed up the process -- if they can.

* Fully-Amortizing Payment:* Almost all mortgages today have fully-amortizing payments (FAPs). This is a payment which, if maintained unchanged through the remaining life of the loan at the then-existing interest rate, will pay off the loan over its remaining life.

The FAP has two components: the interest due the lender, and the principal which is deducted from the balance. The interest portion is calculated as the amount due the lender based on the interest rate and the loan balance. The principal portion is what remains.

* An Example of the Amortization Process:* The loan is for $100,000 at 4% for 30 years. The FAP is $477.42. This number is calculated from a formula that you will find on my web site, or you can use one of many calculators on the web including mine.

To obtain the interest due the lender in month 1, you multiply the balance of $100,000 times the annual interest rate of .04 and divide by 12 to get $333.33. The principal payment is the residual, what remains of the payment after paying the interest. Subtracting $333.33 from $477.42 gives $144.09 as the principal.

Turning to month 2, the new balance is the old balance less the principal payment in month 1, or $99, 855.91. The interest due in month 2 is calculated in the same way as in month 1, but since it uses the new lower balance, it is $.48 lower at $332.85. That makes the principal payment in month 2 $.48 higher at $144.57.

The process repeats each month, with the portion of the FAP allocated to interest gradually declining and the portion allocated to principal gradually rising.

* Additions to the Monthly Payment:* One simple way to accelerate the payoff process is to add some amount to the FAP. 100% of such extra

payments become principal. For example, if the payment in my example was increased by just $10 a month, the loan would pay off 13 months early. If the payment was increased by $100 a month, the loan would pay off 101 months early. I derived these numbers from calculator 2a on my web site.

Such additions to the payment are savings that yield a return equal to the mortgage rate. The mortgage borrower in my example earns 4%. If the $10 extra a month was deposited in a savings deposit, the return today would be 1% or less. That is why paying down the loan balance is a good idea.

* Communicating Your Decision to the Lender:* My mail from borrowers suggests that some are concerned that lenders will grab a piece of any extra payment as interest. This is nonsense, the interest payment due the lender is contractually defined in the note, and cannot be increased. I tell some borrowers that if it makes them feel better, they can include a note with their payment that the extra amount is to be credited to principal. But that is not necessary.

* Occasional Larger Payments:* If you hit the jackpot for $10,000 and use it to pay down your loan balance, you are again making an investment that yields the mortgage rate. There are no other investments available in the market that carry a risk-free return as high.

I have found that some borrowers contemplating a large payment to principal worry about when they must deliver the payment to the lender in order to receive credit in the current month, as opposed to the following month. Lender policies differ in that regard, and it is worth a phone call to find out what the policy is.

A larger worry is that the lender won't give them credit "until the end", meaning until the loan balance has been paid down to the point where it equals the extra payment. This is nonsense, a lender doing this would be committing larceny, yet it keeps popping up in my mail.

* Mortgage Amortization Tools:* Readers can develop an actual amortization schedule using one of my calculators. For straight amortization without extra payments, use my calculator Amortization Schedule Including Tax Savings. To see how amortization is impacted by extra payments of any type, Mortgage Payoff Calculator: Extra Monthly Payments .

*For more information and unbiased mortgage advice, you can contact the professor at The Mortgage Professor .*

Category: Bank

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