After the third month of a 12 month loan,

the numerator is: {(n + ) + (n + ) + (n + )} =

, and

the denominator is: {(n) + (n + 1) + ... + (n + )} =

Therefore, the fraction is numerator/denominator (to the nearest tenth) =

The Rule of 78 tells us to write a sequence using the numerical equivalents for the months of the year. In set notation we would write {1, 2, 3, , 12}. We could also use algebraic notation and write {n, n + 1, ..., n + 11} where n = 1. Clearly this sequence has a beginning and an end so it is finite.

Next, the Rule of 78 tells us to write a series. A series is a summation of quantities based upon a sequence. In this instance if we add the all the individual terms specified by {n, n + 1, ..., n + 11}, the sum is 78. Thus, the name is the rule of 78.