Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using standard amortization, the monthly payment is $161.33. In this example, we will no

Consider a three-year loan (so we'll assume the numbers 1 through 36) for $5,000 with interest at 10% per year. Using standard amortization, the monthly payment is $161.33. In this example, we will not worry about exact or ordinary interest because the total interest to be paid is $808.13. After the fifth month the borrower decides to prepay the whole loan. Under a standard amortization plan the borrower would have paid $198.28 in cumulative interest. However, using the Rule of 78 a lender would calculate the fraction of the total interest based on two series: {(n+35)+(n+34)+(n+33)+(n+32)+(n+31)} ------------------------------------------ {(n)+(n+1)+...+(n+35)} If you add 36, 35, 34, 33, and 32, the sum is a0. If you sum the numbers from 1 to 36, the sum is a1. The fraction (the first sum / the total sum) to the nearest tenth = a2%. The lender will multiply this fraction by the total interest. The cumulative interest = (the percentage calculated above)*($808.13) = $ a3. The difference between the amount paid under a standard amortization plan and the amount paid under a Rule of 78 plan is: $ a4.