Why Mortgage Loans are Fixed Amortized

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January 31, 2014

In a simple interest loan, interest is accrued every day on the outstanding principal balance. The periodic payment amount is fixed, but the breakdown of interest and principal on each payment is determined by the interest balance on the day the payment is received. If a borrower makes their payment early, there will be less interest to pay; therefore, more of their payment will be applied to principal. Conversely, if they pay late, there will be more interest to cover, and so less will apply to principal.

In a fixed amortized loan, the balance accrued on and the breakdown of the payments is preset and not dependent upon the day payments come in. If a payment is applied early, the loan will continue accruing on the principal balance prior to the payment, until the due date is reached. If a payment is late, the loan will lower the amount accrued as if the payment had been made on time. This ensures that no matter what the payment history looks like, when all of the contractually obligated payments have been received, the loan will be paid off (aside for perhaps some amount to account for rounding error).

If a simple interest loan and a fixed amortized loan were set up with otherwise identical parameters, and all payments on the simple interest loan were applied exactly on the due date, the two loans would accrue and apply payments exactly in parallel. This requires that the simple interest loan was never early and never late with a payment by even a single day.

To illustrate the point of why long term loans tend to be fixed amortized loans, we will take a hypothetical loan and set it up both ways. We will further assume that the borrower has a ten day grace period for late charges, and for thirty years she makes each and every payment exactly nine days late. As far as this borrower is concerned, she never got charged a late fee, so she was always on time. We will observe the balance remaining on the two loans at the end of thirty years.

The parameters of the test loan will be:

Principal: \$ 100,000.00

Interest Rate: 10%

Monthly Payment: \$ 877.57

A quick calculation for interest (\$100,000 x 10% / 12 = 833.33) tells us that the principal paid in the first period will only be (\$877.57 - \$833.33) \$44.24, and the per diem interest (for a 30 day month) is (\$833.33/30) \$27.78. So, on our simple interest loan, we will not pay down any interest in the first period if we are late by even as much as two days. Since each payment will be applied nine days late, it is clear to see that this loan will be paying nothing but interest for many months, and will quickly fall behind the fixed amortized loan with regard to paying down principal. For my test, I will backdate the two loans 30 years + 1 month, and set up a recurring transaction to automatically apply the payment nine days late, repeating 360 times. Then, bringing the accrual forward on each loan, I can see what the payoff balances on the two loans are:

Fixed Amortized Payoff: \$6.00

Simple Interest Payoff: \$4,728.16

The final payment on the fixed amortized loan is nothing more than 360 fractional cents due to the monthly payment amount being rounded down, and the accumulation of 30 years of compound interest on those cents. Many lending companies would write this difference off.

It is clear to see why it's necessary for these mortgages to be fixed amortized loans. The customer who made every payment for 30 years within the grace period and never had to pay a late fee is likely to be quite shocked to discover that she owes the equivalent of more than five months worth of additional payments on a loan that she thought she had paid off. Instead of a mortgage burning party, she is presented with a balloon payment of nearly 5% of her original balance. Not my idea of fun.