# Unpacking Loan Jargon To Calculate True Cost

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By Jack Guttentag
Saturday, April 28, 2007

Q: I have recently heard advertisements for mortgages with the disclaimer that the "payment rate is not the interest rate." How does that work?

A: The interest rate is the rate used to calculate the amount of interest the borrower owes the lender each month. The payment rate is the rate used to calculate the amount of the payment the borrower is obliged to make each month. On most mortgages, they are the same, which is why it may be confusing when they are different.

Consider a 30-year mortgage for \$100,000 at an interest rate of 6 percent. The interest due from the borrower in the first month is 6 percent of 100,000, divided by 12, which comes out to \$500. Using 6 percent as the payment rate, the monthly payment including interest and principal is \$599.56. (This is calculated using a formula that is too complex to show here but is available on my Web site.)

The formula assumes that the payment rate and interest rate are the same. It calculates the fully amortizing payment, which is the payment that will pay off the balance completely. If the borrower in this example pays \$599.56 every month, the 360th payment will be the last.

Now let's assume that the interest rate remains at 6 percent but that the payment rate is only 3 percent. Using the same formula, the payment at 3 percent is \$421.61, but because the payment rate is below the interest rate, this payment is not fully amortizing. The borrower pays \$421.61, but because the interest rate remains at 6 percent, the interest due the lender continues to be \$500. The shortfall of \$78.39 must be added to the loan balance. The shortfall is called "negative amortization."

A payment rate below the interest rate is always temporary. Because mortgages are designed to be paid off in full over their term, at some point the payment must be recalculated at the interest rate to be fully amortizing over the remaining life of the loan.

In my example, assuming recalculation after five years, the payment would increase to \$679.55, which would pay off the \$105,469 balance at that time over the remaining 25 years. If payments are not recalculated until the end of 10 years, the balance would reach \$112,847, and the monthly payment required to amortize it over 20 years would be \$808.48.

A small-type disclaimer saying the "payment rate is not the interest rate" almost certainly was attached to marketing materials for an option adjustable-rate mortgage. This has been a popular mortgage because of its low initial payments. In 2005 and 2006, about \$500 billion in option ARMs was written, much of it to borrowers who did not understand the difference between interest rate and payment rate. Many borrowers have been catching on recently and wondering whether they made a mistake.

The confusing thing about the most widespread version of the option ARM is that the payment rate and interest rate are the same in the first month. The interest rate on this ARM adjusts monthly, however, and in month two, that rate jumps. It can be 3 percentage points or more above the payment rate starting in month two, remaining there for up to 10 years, but a day of reckoning is inevitable.

The option ARM has been very aggressively marketed. The focus has been low initial payments, with the inevitable rise in payments deemphasized or ignored.

Existing disclosure rules provide no help to borrowers.

Recently, a group of regulators from five federal agencies expressed concern that many borrowers taking option ARMs were getting in over their heads without realizing it. Acknowledging that amending the disclosure laws would take too long, they proposed that lenders provide improved disclosure on their own. The disclaimer about the payment rate not being the same as the interest rate could be an attempt to do so. If so, it is pitifully inadequate, though it may provoke some borrowers to seek more information elsewhere.

Jack Guttentag is professor of finance emeritus at the Wharton School of the University of Pennsylvania. He can be contacted through his Web site,http://www.mtgprofessor.com.