Section5.4567

# Section5.4567 - Refinancing A Loan The Sum of Digits...

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Refinancing A Loan – The Sum of Digits Method (section 5.4) There are still a few Canadian lending institutions that use the sum-of-digits method (also called the “Rule of 78”) when determining the outstanding balance on a loan this method is an approximation to the amortization method the main difference is that we determine the interest portion of each payment by taking a defined proportion of the total interest paid on the loan

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Method Original Loan = A Term of loan = n-periods Interest rate on loan = i Thus, Periodic payment, R = i n a A | Define 1. I = total interest paid on loan = nR - A 2. sum of digits 1 to n, s n =
The interest paid column looks like: k R I k P k B k 0 -- -- -- A 1 R I s n I n = 1 2 R I s n I n - = 1 2 : : : k R I s k n I n k + - = 1 : : : n −1 R I s I n n = - 2 1 n R I s I n n = 1 0 total nR I = nR − A A

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Example 5.4.1 A loan of \$9000 is to be repaid with 6 equal monthly payments at j 12 = 12%. Set up a repayment schedule using the sum of digits method. Solution to 5.4.1
Note The sum of digits method always leads to an outstanding balance that is higher than that obtained by using the amortization method so, if you pay back your loan early OR if you refinance the loan at any point in time, you are penalized under the sum of digits method As of January 1, 1983, this method became illegal for consumer loans issued by Canadian chartered banks but it can still be used (and sometimes is used) by car dealers and furniture companies

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Section5.4567 - Refinancing A Loan The Sum of Digits...

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