a simple fraction (as with 12/78) consists of a numerator (the top number, 12 in the example) and a denominator (the bottom number, 78 in the example). the denominator of a rule of 78 loan is the sum of the digits, the sum of the number of monthly payments in the loan. for a twelve-month loan, the sum of numbers from 1 to 12 is 78 (1 + 2 + 3 + . . . +12 = 78). for a 24-month loan, the denominator is 300. the sum of the numbers from 1 to n is given by the equation n * (n+1) / 2. if n were 24, the sum of the numbers from 1 to 24 is 24 * (24+1) / 2 = 12 x 25 = 300, which is the loan's denominator, d.