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rule of 78 method and level method

Lynn had a $2,000 personal loan at 9 1/2% for 18 months. Suppose that she is given the choice between the level method and the rule of 78 method and that she wants to pay off the remaining balance after a year of making monthly payments. Which method would she choose, and what difference in interest would she pay?

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Michael W. | Credentialed Mathematics TeacherCredentialed Mathematics Teacher
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The rule of 78ths is designed to pay the lender his interest more rapidly than the level method. It tilts the table in the lender's direction.
It is called the rule of 78ths because if you add the month or payment numbers from 1 to 12 you get 78. The way it works is you calculate the monthly payment and the interest to be paid over the life of the loan by the usual method.  However the allocation of the payment to principal and interest is altered in the lender's favor as follows:
In the first month of a 12 month loan, the lender is allowed to collect 12/78 times the total interest to be paid for the term of the loan. In the second month, the lender collects 11/78 time the total loan interest on the loan. In subsequent months, 10/78, 9/78, 8/78, 7/78, 6/78, 5/78, 4/78, 3/78, 2/78, and 1/78 of the total loan interest is collected.
The only time this affects the borrower significantly, is in the event of an early loan payoff. In this case the lender benefits because less of the loan principal has been credited under this method than would have been under the usual method. Thus the lender pays more interest and more in total than would have been due otherwise.
On an 18 month loan, the numbers from 1 to 18 add up to 171. On the first payment the lender collects 18/171 of the total loan interest. Then 17/171, 16/171 and so on.
You can apply the payment calculator formula, calculate the total interest to be earned by the lender and determine how much interest would be collected under the given scenario by this method and by the level method.