A company borrowed $10,000 by signing a 180-day promissory note at 9%. The total interest due on the maturity date is:
A. $900
B. $75
C. $450
D. $300
E. $1,800
The correct answer and explanation is :
To determine the interest due on a 180-day promissory note at 9% annual interest, we use the simple interest formula:
$$
\text{Interest} = P \times r \times t
$$
Where:
- $P$ = principal (amount borrowed) = \$10,000
- $r$ = annual interest rate = 9% = 0.09
- $t$ = time in years. Since the loan is for 180 days, we convert this to a fraction of a year:
$$
t = \frac{180}{360} = 0.5 \quad \text{(using a 360-day year, common in financial calculations)}
$$
Now calculate:
$$
\text{Interest} = 10,000 \times 0.09 \times 0.5 = 450
$$
Correct Answer: C. \$450
Explanation (300 words):
In financial transactions, especially short-term loans, it’s standard to calculate interest using the simple interest formula:
$$
\text{Interest} = P \times r \times t
$$
In this scenario, a company takes a 180-day promissory note for \$10,000 at an annual interest rate of 9%. A promissory note is a written agreement where one party promises to pay a specific amount of money to another, typically with interest, by a certain date. This form of debt instrument is commonly used for short-term borrowing.
The formula requires the time in years, but because the loan duration is 180 days, and financial institutions often assume a 360-day year for such calculations (called a “banker’s year”), we convert 180 days to a fraction of a year:
$$
t = \frac{180}{360} = 0.5 \text{ year}
$$
With this, the interest calculation becomes straightforward:
$$
\text{Interest} = \$10,000 \times 0.09 \times 0.5 = \$450
$$
This means when the note reaches its maturity date, the company will owe \$10,000 (the principal) plus \$450 in interest, for a total of \$10,450.
This approach ensures transparency in short-term borrowing, helping companies plan their repayments accurately and avoid late fees or financial mismanagement.
Thus, the correct answer is C. \$450.