The thing that most borrowers know about their mortgages is the amount of the initial scheduled payment. This is the amount they are obliged...

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The thing that most borrowers know about their mortgages is the amount of the initial scheduled payment.

This is the amount they are obliged to pay each period under the terms of the mortgage contract. They know that failure to pay that amount is a violation of the contract, leading to late charges, delinquency reports and foreclosure. While borrowers know the amount, they are often hazy about how it is calculated and what it includes. I will illustrate the possibilities related to a \$100,000 loan at 6 percent.

In the simplest possible case, the scheduled payment includes only interest until the final payment, when it includes repayment of the balance.

The interest payment each month is 0.06/12, or 0.005, multiplied by \$100,000, which equals \$500. The final payment, assuming the borrower paid only interest throughout, would be \$100,500.

Most mortgages written during the 1920s were of this type, usually with terms of five or 10 years.

Their weakness is that they must be refinanced at term, which during the Depression of the 1930s became difficult because property values and borrower incomes had fallen.

The notion took hold that it was prudent for borrowers to pay down the balance over time by making a mortgage payment larger than the interest. This additional amount is called the principal payment.

The principal payment is always a residual — the total payment less the interest. If the borrower in the example paid \$600, the \$500 of interest would be deducted, leaving \$100 as the principal payment. If the borrower paid \$700, the principal payment would be \$200.

Including principal in the scheduled payment requires a rule for determining what that payment is. The most obvious rule is to pay back equal amounts of principal every month. If our sample loan is for 30 years, we divide \$100,000 by 360 to get a principal repayment of \$277.78 a month.

Loans of this type have existed, most recently in New Zealand, but they have a serious drawback. The scheduled payment that includes a fixed amount of principal every month starts high — too high for many borrowers — and ends low because of the decline in interest. In month one, the scheduled payment is \$277.78 plus \$500, or \$777.78. In month 360, it is \$277.78 plus \$1.39, or \$279.17.

So some unknown pundit reasoned as follows: “If payments beginning at \$777.78 and declining every month to \$279.17 will pay off this loan, there must be some amount in between, which, if made every month without change, would do the same.”

The reasoning is correct — the amount (\$599.56 in my example) is called the fully amortizing payment.

The fully amortizing payment is calculated from an equation that my editor says does not belong in a family publication. It is on my Web site (www.mtgprofessor.com) under “Formulas.” But you don’t need the equation; financial calculators have programmed it so you can derive an answer in seconds, whereas solving the equation takes minutes.

The only way to reduce the initial payment is to reduce the principal payment.

On mortgages with an interest-only option, the scheduled payment is the interest payment for the length of the interest-only period, usually five to 10 years. After that, the scheduled payment becomes the fully amortizing payment.

On option ARMs, borrowers have the rare privilege of selecting their own scheduled payment during the first five or 10 years.

They can select the fully amortizing payment over either 15 or 30 years, the interest-only payment, or a “minimum” payment that is less than the interest.

Most borrowers select the last, and sometimes find themselves in trouble when their scheduled payment increases in future years.

If the borrower has agreed to escrow property taxes and homeowners insurance, most lenders treat the monthly escrow payments as if they are also part of the scheduled payment; if the escrow payment is short, the payment is considered delinquent.

A borrower can start down a slippery path to foreclosure by failing to pay required escrows.

The writer is professor emeritus of finance at the Wharton School of the University of Pennsylvania: jguttentag@mtgprofessor.com.