The Mortgage Interest Rate Versus the Payment Rate
April 2, 2007, Revised August 27, 2011

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

## Definition of Interest Rate and Payment Rate

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 one and 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%. The interest due from the borrower in the first month is .06 times 100,000 divided by 12, or \$500. Using 6% as the payment rate, the monthly payment is \$599.56. This is calculated from an equation in Formulas.

The formula is derived on the assumption that the payment rate and interest rate are the same. It calculates the "fully amortizing payment", which is the payment that will amortize the balance over the term. If the borrower in my example pays \$599.56 every month, the 360th payment will be the last.

## When the Payment Rate Is Below the Interest Rate

Now let’s assume that the payment rate is only 3%. Using the same formula, the payment at 3% is \$421.61, but since the payment rate is below the interest rate, this payment is not fully amortizing. The borrower is now required to pay \$421.61 but because the interest rate remains at 6%, 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. All mortgages, excepting only "balloon loans", are designed to be paid off in full over their term. At some point, therefore, the payment must be recalculated at the interest rate to be fully amortizing over the remaining life of the loan.

In my example, assuming this happened after 5 years, the payment would increase to \$679.55, which will pay off the \$105,469 balance at that time over the remaining 25 years. If it did not happen for 10 years, the balance would reach \$112,847, and the payment required to amortize it over 20 years would be \$808.48.

## Low Payment Rates on Option ARMs

In 2005 and 2006, lenders wrote about \$500 billion of option ARMs, which were very attractive because of their low initial payment r ates. It is clear that many borrowers who took option ARMs did not understand the difference between interest rate and payment rate. No one bothered to explain it to them at the time, and many paid a bitter price in subsequent years. .

The confusing thing about the most widespread version of the option ARM was that the payment rate and interest rate were the same in month one -- it was only in month 2 that they diverged. The interest rate on this ARM adjusted monthly, and in month two it could jump 3 percentage points or more above the payment rate, remaining there for up to 10 years before the day of reckoning. See Tutorial on Option ARMs.

The option ARM was very aggressively merchandised. The focus was the low initial payments, with the inevitable rise in payments in the future deemphasized or ignored altogether. Existing disclosure rules provided no help to borrowers. Default rates after the financial crisis were horrendous, and none were written after 2007.