#### Definition:

Rule of 78 is a method of computing yearly interest-refund on a permanent loan installment basis, where the amount should be paid off before the duration date. This method assures that if the borrower repays the loan amount earlier, then the lender can make a guaranteed profit.

#### Formula:

(U * (U + 1)) \ (T * (T + 1)) = Rule of 78s refund decimal * F = Refund
###### Where,

U = Unearned period
T = Total period
F = Finance charge
#### Example :

A man agreed 12 month contract which has been prepaid at 3 months and unearned periods are 9 months with a finance charge of $100.00. Find out the refund amount for the loan using Sum of the Digits Method?

##### Given,

T = 12 months, F = $100.00 U = 9 months

##### To Find,

Loan Refund (F) using Sum of the Digits Method

##### Solution :

(U * (U + 1)) \ (T * (T + 1)) = Rule of 78s refund decimal * F = Refund
Refund = [(9* (9 + 1)) / (12 (12 + 1))] * 100
= [(9 * 10) / (12 * 13)]* 100 = [90 \ 156]*100
= [.5769]*100
= $57.69