# Prepayment

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**Prepayment** is when a borrower pays off all or part of the loan before the maturity date. Prepayment can occur for a variety of reasons such as a lump sum payment, refinancing, or a sale of the property. This can be beneficial to a borrower because it reduces the amount of interest they have to pay over the life of the loan.

- Lump Sum Payment - This is when a borrower makes a payment in full to cover the remaining balance of the loan. This is beneficial for borrowers because it eliminates the need for monthly payments.
- Refinancing - This is when a borrower takes out a new loan to pay off an existing loan. This allows the borrower to take advantage of lower interest rates and payment terms.
- Sale of the Property - This is when a borrower sells the property and uses the proceeds from the sale to pay off the remaining balance of the loan. This is beneficial for borrowers because it eliminates the need for monthly payments.

Prepayment can be beneficial to borrowers because it reduces the amount of interest they have to pay over the life of the loan. It also eliminates the need for monthly payments and allows borrowers to take advantage of lower interest rates and payment terms.

## Example of Prepayment

Let's say you owe $10,000 on a loan with an interest rate of 5% and a term of 5 years. If you decide to make a lump sum payment of $10,000 you would save $2,500 in interest payments over the life of the loan.

The formula for calculating the amount of interest saved from a prepayment is\[Int\_saved = \frac{Interest\_Rate \times Loan\_Amount \times Remaining\_Term}{12}\]

In this example, the amount of interest saved would be\[Int\_saved = \frac{0.05 \times 10,000 \times 60}{12} = 2,500\]

## Formula of Prepayment

Let $P$ be the original principal loan amount, $r$ be the interest rate, and $n$ be the number of payments. The formula for calculating the amount of interest saved by prepaying a loan is\[Interest\ saved\ = \ P \cdot \left( \sum_{i=1}^n \frac{r}{12} \cdot (1+\frac{r}{12})^{n-i}\right) - \ P \cdot \left( \sum_{i=1}^n \frac{r}{12} \cdot (1+\frac{r}{12})^{n-1-i}\right) \]

This formula calculates the difference between the total amount of interest paid on the original loan and the total amount of interest paid on the loan after the prepayment. This allows borrowers to see how much they would be able to save by prepaying their loan.

## When to use Prepayment

Prepayment can be used in a variety of situations, such as when a borrower needs to pay off a loan quickly, when they need to take advantage of lower interest rates or payment terms, or when they need to free up cash flow.

- Need to Pay Off Loan Quickly - This is when a borrower needs to pay off a loan quickly, either to avoid additional fees or to improve their credit score.
- Need to Take Advantage of Lower Interest Rates or Payment Terms - This is when a borrower needs to take advantage of lower interest rates or payment terms that are available in the market.
- Need to Free Up Cash Flow - This is when a borrower needs to free up cash flow for other uses.

## Types of Prepayment

- Prepayment Penalty - This is a fee that is imposed by lenders when a borrower pays off a loan before its maturity date. This is designed to protect lenders from losing money due to early repayment.
- Prepayment Discount - This is a discount that is offered by lenders to borrowers who pay off a loan before its maturity date. This is usually offered as an incentive to borrowers to pay off the loan early.
- Prepayment Privilege - This is a clause in a loan agreement that allows borrowers to pay off part or all of their loan before the maturity date without incurring a penalty.

## Steps of Prepayment

- Calculate the Prepayment Penalty - When a borrower prepays a loan, they may have to pay a prepayment penalty. This penalty is calculated by multiplying the remaining balance by a certain percentage.
- Calculate the Savings - Once the prepayment penalty has been calculated, the borrower can calculate the savings from prepaying the loan. This is done by subtracting the prepayment penalty from the remaining balance of the loan.
- Submit the Payment - Finally, the borrower will submit the payment in full to the lender. This will eliminate the remaining balance of the loan and reduce the amount of interest they have to pay over the life of the loan.

## Advantages of Prepayment

- Lower Interest Rate - This allows borrowers to take advantage of lower interest rates and payment terms.
- Reduced Payment - This reduces the amount of interest they have to pay over the life of the loan.
- Eliminate Monthly Payments - This eliminates the need for monthly payments and allows borrowers to save money.

Prepayment can be beneficial to borrowers because it can reduce the amount of interest they have to pay over the life of the loan, eliminate the need for monthly payments, and allow borrowers to take advantage of lower interest rates and payment terms. It can also provide borrowers with the flexibility to pay off their loan earlier than the maturity date.

## Limitations of Prepayment

Despite the benefits of prepayment, there are some potential drawbacks as well.

- Prepayment Penalties - Many lenders have prepayment penalties that are charged if a borrower pays off the loan before the maturity date. These penalties can be significant and should be taken into account when considering prepayment.
- Tax Implications - Prepayment of a loan can have an effect on the borrower's tax liability. In some cases, prepayment can result in a tax liability that would not have been incurred if the loan was paid off in full at the end of the term.
- Opportunity Cost - Paying off a loan early can also result in an opportunity cost for the borrower. This is because the money that is used to pay off the loan could be invested elsewhere and earn a return.

- Prepayment Penalties - This is when a lender charges a fee if a borrower pays off all or part of their loan before the maturity date. This is designed to protect the lender from losing money if the borrower pays off the loan too quickly.
- Prepayment Privileges - This is when a lender allows a borrower to make additional payments without penalty. This is beneficial for borrowers because it allows them to pay off their loan sooner and save money on interest.
- Prepayment Calculations - This is when a lender calculates the amount of interest a borrower will save if they make an additional payment. This is beneficial for borrowers because it helps them understand the impact of making additional payments.

Prepayment penalties, privileges, and calculations are other approaches related to prepayment. Prepayment penalties protect the lender from losing money if the borrower pays off the loan too quickly. Prepayment privileges allow borrowers to make additional payments without penalty and save money on interest. Prepayment calculations help borrowers understand the impact of making additional payments.

## Suggested literature

- Schwartz, E. S., & Torous, W. N. (1989).
*Prepayment and the valuation of mortgage‐backed securities*. The Journal of Finance, 44(2), 375-392. - Patrick, V. M., & Park, C. W. (2006).
*Paying before consuming: Examining the robustness of consumers’ preference for prepayment*. Journal of Retailing, 82(3), 165-175. - Stanton, R. (1995).
*Rational prepayment and the valuation of mortgage-backed securities*. The Review of financial studies, 8(3), 677-708.