Answer to Question #275206 in Financial Math for Jay

Question

Mike Marquez purchased a lawn tractor for Php 9,000. He made a down

payment of Php 1,000 and financed the rest at 7% payable in 24 months. He paid off

the loan at the end of the fifteenth months. Find the amount of his refund using the rule

of 78s.

Answer 1

The Rule of 78 is a method used by some lenders to calculate interest charges on a loan. The Rule of 78 requires the borrower to pay a greater portion of interest in the earlier part of a loan cycle, which decreases the potential savings for the borrower in paying off their loan.

For a one year loan, the total number of digits is equal to 78, which explains the term the Rule of 78. For a two year loan, the total sum of the digits would be 300.

According to the given information, the interest amount is to be calculated as follows:

Working:

$\frac{(U×(U+1))}{(T×(T+1)) }=$ Rule of 78's refund decimal×F=Rebate

where:

T = 24 months

U = Unearned Months = 24 −15 = 9 months

So, using the above formula, the rebate will be:

F = Finance Charges = $1,198.45

$\frac{(9×(9+1))}{(24×(24+1))} =\frac{9×10}{24×25}=0.15\\=0.15×\$1,198.45\\=\$179.77$