A certain retailer\'s credit contract designates the rule of 78 for computing un

Question

A certain retailer's credit contract designates the rule of 78 for computing unearned interest and imposes a "prepayment penalty." In case of any payoff earlier than the due date, they writ charge an additional 10% of the original finance charge. Find the least value of k (remaining payments after payoff) that would result in any net savings in the case of 36 payments originally scheduled. In order to result in any savings, the payoff must be at least months early. (Round up to the nearest integer as needed.)

Explanation / Answer

For this question first of all you should know the rule of 78 which is in general the idea that more weight is given to the payment's which are done earlier and as a result borrower has to pay more incase of prepayment made to the lender.

Here is the equation you are looking for as above: Now we can substitute the value as given in the table of k or prepayment ranging from 1 to 35.

So, k should be minimum 17 as marked bold and underlined to get the benefit as you will get unearned interest more than 1.

Unearned interest = Total agreed finance charges * Number of months paying off early (no of months paying of early + 1) / n(n+1) or u = f * k(k+1)/n(n+1) 10%*k(k+1)/36(36+1)

Here is the equation you are looking for as above: Now we can substitute the value as given in the table of k or prepayment ranging from 1 to 35.

1-36 = k n Finance charge Now applying the formula as above 1 36 10% 0.00540541 2 36 10% 0.02105263 3 36 10% 0.04615385 4 36 10% 0.08 5 36 10% 0.12195122 6 36 10% 0.17142857 7 36 10% 0.22790698 8 36 10% 0.29090909 9 36 10% 0.36 10 36 10% 0.43478261 11 36 10% 0.51489362 12 36 10% 0.6 13 36 10% 0.68979592 14 36 10% 0.784 15 36 10% 0.88235294 16 36 10% 0.98461538 17 36 10% 1.09056604 18 36 10% 1.2 19 36 10% 1.31272727 20 36 10% 1.42857143 22 36 10% 1.66896552 24 36 10% 1.92 25 36 10% 2.04918033 26 36 10% 2.18064516 27 36 10% 2.31428571 28 36 10% 2.45 29 36 10% 2.58769231 30 36 10% 2.72727273 31 36 10% 2.86865672 32 36 10% 3.01176471 33 36 10% 3.15652174 34 36 10% 3.30285714 35 36 10% 3.45070423

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