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The payment of a debt in equal future installments is an application of the present value of an ordinary annuity. The amount of each installment includes interest and principal. Theoretically, the interest portion of each payment should be based on the unpaid principal balance. Every accountant should have learned this fact in their Principles of Accounting class.
However, in constructing a debt payment schedule, many financial institutions do not employ the unpaid principal balance approach. Instead, the rule-of-78 method is used. The rule-of-78 method is actually the sum-of-the-months'-digits method in disguise. The name of the rule-of-78 method derives from the fact that the sum of 1 through 12 is equal to 78. It is a very clever approach to penalize the borrower who pays off the debt before it has matured.
To apply the rule-of-78 method, one would first compute the total financial charges by multiplying the amount of each installment by the total number of payments and then subtracting the principal from the product. Secondly, the method would calculate a fraction for each time period. The denominator of each fraction is obtained by adding the months' digits for the life of the debt. The numerator which, changes each period, is the months digits in reverse order. Thirdly, the interest portion of each payment is obtained by multiplying the total financial charges by the fraction. The principal portion is then determined by subtracting the interest portion from the amount of each installment.
The problem with the rule-of-78 method is that it allocates more financial charges in the earlier periods than the unpaid principal balance method. Therefore, the remaining principal balance of a debt amortization schedule under the rule-of-78 method would be...