How does the rule of 78 work?
If you have a 24-month loan that is paid in full with 10 months remaining, using the Rule of 78, would you expect a refund? Why or why not? Use a specific example in your explanation.
The Rule of 78, also known as the Sum of the Digits method, is a technique used to calculate prepayment penalties or refunds for loans that are paid off before their scheduled term.
To understand how the Rule of 78 works, consider a simplified example with a 24-month loan. In this case, the sum of the digits for the loan term is calculated as follows: 1+2+3+...+24 = 300. Each month's payment is assigned a percentage equal to the number of months remaining divided by the sum of the digits. For example, at the beginning of the loan, the first month's payment would be 24/300 = 8% of the total payment.
Now, let's suppose that after making regular payments for 14 months, you decide to pay off the loan in full with 10 months remaining. To calculate the prepayment penalty or refund using the Rule of 78, follow these steps:
1. Determine the total amount of interest paid to date: Add up the percentage corresponding to each month's payment made so far. In this case, it would be 8% (first month) + 7.33% (second month) + 6.67% (third month), and so on until the 14th month.
2. Calculate the total amount due based on the terms of the loan: Multiply the original loan balance by the sum of the digits (in this case, 300) to get the total amount due.
3. Compare the total amount of interest paid to the total amount due: If the total amount of interest paid is less than the total amount due, there would be a prepayment penalty, which means you would not receive a refund. Conversely, if the total amount of interest paid is greater than the total amount due, you would be entitled to a refund.
In this example, let's assume that after 14 months, you have paid $1,400 in interest. To calculate the total amount due, given an original loan balance of $10,000, you would multiply $10,000 by 300, resulting in $3,000,000.
Comparing the total amount of interest paid ($1,400) to the total amount due ($3,000,000), we can see that the interest paid is significantly less than the total amount due. Therefore, according to the Rule of 78, you would not expect a refund.