Question

What is meant by a bank loan that is called a 7 percent discount?

Short answer

A 7 percent discount bank loan refers to a loan where the bank deducts a 7% interest in advance from the principal amount before disbursing the loan to the borrower. In this case, the borrower receives an amount equal to the principal amount minus 7% of the principal. At the end of the loan term, the borrower is required to repay the full principal amount. For example, for a $10,000 loan with a 7% discount rate, the borrower would receive $9,300 and be required to pay back $10,000 at the end of the loan term.

Step-by-step solution

Understand the concept of a discount loan

A discount loan is a type of loan where the interest is deducted (discounted) from the principal amount before the loan is disbursed to the borrower. The borrower will then repay the full amount of the loan at the end of the loan term.

Identify the key variables

For a 7 percent discount bank loan, the key variables are: 1. Principal amount (P) 2. Interest rate (7%) 3. Loan term (e.g., in months or years)

Calculate the interest amount

To calculate the interest amount, the interest rate (7%) must be multiplied by the principal amount (P). Interest Amount = Principal Amount * Interest Rate = P * 7%

Calculate the disbursed amount

The amount disbursed to the borrower is the principal amount minus the interest amount. Disbursed Amount = Principal Amount - Interest Amount

Express the discount loan in terms of principal and interest

The 7 percent discount loan can be expressed as follows: The borrower receives an amount equal to the principal amount (P) minus 7% of P as the loan. The borrower will then repay the full principal amount (P) at the end of the loan term. To see how this works, let's use an example:

Example:

Suppose a borrower requested a $10,000 loan with a 7% discount rate for a 1-year term. We need to calculate how much the borrower will receive from the bank and how much they will be required to pay at the end of one year.

Calculate the interest amount

Interest Amount = Principal Amount * Interest Rate = \(10,000 * 7% = \)700

Calculate the disbursed amount

Disbursed Amount = Principal Amount - Interest Amount = \(10,000 - \)700 = $9,300

Determine the repayment amount

At the end of the loan term, the borrower will be required to repay the full principal amount, which is $10,000. In conclusion, a bank loan called a 7 percent discount means that the bank deducts a 7% interest in advance from the principal amount before disbursing the loan to the borrower. In this example, the borrower would receive \(9,300, and they would be required to pay back \)10,000 at the end of the loan term.

Key concepts

Interest Rate Calculation

Understanding how interest is calculated on loans is essential for both borrowers and lenders. When dealing with a discount loan, such as the 7 percent discount example, interest calculation takes on a slightly different format than the typical loan. Instead of accruing interest over the loan term, the interest is deducted upfront from the principal amount. This interest is calculated by multiplying the principal amount by the interest rate.

For our given example, with a principal amount of \(10,000 and an interest rate of 7%, the calculation would be as follows:
\[ \text{Interest Amount} = \text{Principal Amount} \times \text{Interest Rate} = \$10,000 \times 7\% = \$700 \]
This means that \)700 represents the cost of borrowing the money, which is withheld by the lender immediately, reducing the amount of cash the borrower receives.

Principal Amount

The principal amount in any loan scenario represents the initial sum of money borrowed before any interest or fees are applied. In the context of a discount loan, it is crucial to understand that the principal amount is the amount that must be repaid by the borrower at the end of the loan term, regardless of the initial disbursement.

In our scenario with a 7 percent discount loan, even though the borrower only receives \(9,300, they are still on the hook to pay back the full principal amount of \)10,000 at the end of the term. This setup can affect the overall cost of the loan, as the effective interest rate may be higher than the nominal rate when taking into account the reduced funds available to the borrower.

Loan Disbursement

Loan disbursement refers to the process of the lender releasing the borrowed funds to the borrower. In the case of a discount loan like the one we're discussing, the disbursement amount is the principal amount minus the interest charged upfront.

As per our example, after calculating the interest amount of \(700, we can determine the disbursement amount by subtracting this interest from the principal amount of \)10,000:
\[ \text{Disbursed Amount} = \text{Principal Amount} - \text{Interest Amount} = \$10,000 - \$700 = \$9,300 \]
Thus, the borrower will receive \(9,300 but must be aware that the obligation still stands to repay the full \)10,000 at the loan's maturity. This concept is critical since it influences the borrower's cash flow and the actual amount of money they have at their disposal during the loan term.