# Residual interest

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**Residual interest** is a type of interest that is due on the principal balance of a loan when the loan is paid off before the interest period is over. In other words, it is the amount of interest that is not accrued or paid before the principal is paid in full. This type of interest is typically found in installment loans, such as car loans, mortgages, or personal loans.

Residual interest is calculated by taking the interest rate of the loan and multiplying it by the number of days that the loan was outstanding. For example, if a loan has a 5% interest rate and is outstanding for 30 days, the residual interest would be 5% x 30 days or 1.5%. This amount would be added to the balance of the loan and would be due when the loan is paid off.

In most cases, the borrower will be required to pay the residual interest in addition to the remaining principal balance when the loan is paid off. This ensures that the lender receives the full amount of interest due on the loan. Additionally, borrowers may be required to pay a penalty for early repayment if the residual interest is not paid in full.

## Example of Residual interest

For example, if a borrower takes out a loan with an interest rate of 7% and a term of six months, and pays the loan off after three months, the residual interest would be calculated as follows:

7% x 3 months = 2.1%

The borrower would then be responsible for paying the remaining principal balance plus the 2.1% residual interest when the loan is paid off.

## Formula of Residual interest

The formula for calculating residual interest is: Residual Interest = Interest Rate x Number of Days Outstanding. In this formula, the Interest Rate is the annual interest rate of the loan and the Number of Days Outstanding is the number of days that the loan was outstanding before it was paid in full.

## When to use Residual interest

Residual interest is most commonly used in situations where a borrower needs to pay off a loan before the end of the interest period. This could be due to a variety of reasons, such as the borrower being able to pay off the loan early or needing to refinance the loan. Residual interest is also used when a loan is sold or transferred to another party before the end of the interest period. In these cases, the residual interest is paid to the original lender or transferred to the new lender.

## Types of Residual interest

**Simple Interest**: Simple interest is calculated on the original principal amount of the loan and does not take into account any additional payments that may have been made. This type of interest is typically used for short-term loans or for loans with a fixed interest rate.**Compound Interest**: Compound interest is calculated on the original principal amount of the loan as well as any additional payments that have been made. This type of interest is typically used for long-term loans or for loans with a variable interest rate.

## Steps of Residual interest

**Step 1**: Calculate the total interest due on the loan by multiplying the interest rate of the loan by the number of days the loan has been outstanding.**Step 2**: Calculate the total amount of interest that has already been paid on the loan by subtracting all prior payments from the total interest due.**Step 3**: The remainder is the residual interest due on the loan and must be paid when the loan is paid off.**Step 4**: If the residual interest is not paid in full, the borrower may be subject to a penalty for early repayment.

## Advantages of Residual interest

- Residual interest ensures that lenders receive the full amount of interest due on the loan.
- Residual interest helps to protect lenders from losses due to early repayment of loans.
- It encourages borrowers to adhere to the terms of the loan and make their payments on time.

## Disadvantages of Residual Interest

- Borrowers may be required to pay a penalty for early repayment if the residual interest is not paid in full.
- It can be difficult to calculate the exact amount of residual interest that is due on the loan.

Residual interest can be a costly expense for borrowers, especially if the loan is paid off early. Additionally, it can be difficult to calculate the exact amount of residual interest due, as it depends on the interest rate and the exact number of days the loan was outstanding. Furthermore, the penalty for early repayment can be significant, and may be more than the amount of interest due.

There are several other approaches that can be taken when dealing with residual interest. For example, a lender may choose to waive the residual interest or offer a discounted rate. Additionally, the lender may agree to prorate the interest, which is a practice of dividing the interest due on the loan over the number of payments that the loan is outstanding for.

In addition, lenders may also offer a "no prepayment penalty" policy, which allows the borrower to pay off the loan early without penalty. This is beneficial for borrowers as it allows them to save money by avoiding the interest that would have accrued on the loan had it not been paid off early.

In summary, there are several approaches to dealing with residual interest. These include waiving the residual interest, offering a discounted rate, prorating the interest, or offering a "no prepayment penalty" policy. Each of these approaches has its own advantages and disadvantages, and should be carefully considered before deciding which one is the best option for a particular loan.

## Suggested literature

- Van Brunt, K. (1994).
*Tax Aspects of Remic Residual Interests*. Fla. Tax Rev., 2, 149. - Kandil, F. A., Lord, J. D., Fry, A. T., & Grant, P. V. (2001).
*A review of residual stress measurement methods-a guide to technique selection*.