A company borrowed $10,000 by signing a 180-day promissory note at 9%. The maturity value of the note is:
A. $10,450
B. $10,900
C. $10,075
D. $11,800
E. $10,300
The correct answer and explanation is :
To find the maturity value of a promissory note, we use the formula:
$$
\text{Maturity Value} = \text{Principal} + \text{Interest}
$$
Step 1: Identify the values given
- Principal (P) = \$10,000
- Time (T) = 180 days
- Rate (R) = 9% annual interest
- Use a 360-day year (common in financial math)
Step 2: Calculate the interest
We use the simple interest formula:
$$
\text{Interest} = P \times R \times \frac{T}{360}
$$
Substitute the known values:
$$
\text{Interest} = 10,000 \times 0.09 \times \frac{180}{360}
$$
$$
\text{Interest} = 10,000 \times 0.09 \times 0.5 = 10,000 \times 0.045 = 450
$$
Step 3: Calculate the maturity value
$$
\text{Maturity Value} = 10,000 + 450 = \boxed{10,450}
$$
Final Answer: A. \$10,450
Explanation (300 words):
A promissory note is a financial instrument in which a borrower agrees to repay a specific sum of money at a future date, with interest. In this case, the company borrows \$10,000 for 180 days at an annual interest rate of 9%. The goal is to determine the total amount the company must repay at the end of the term—known as the maturity value.
Interest on such short-term notes is typically calculated using the simple interest formula:
$$
\text{Interest} = P \times R \times \frac{T}{360}
$$
where:
- $P$ is the principal (\$10,000),
- $R$ is the annual rate (9% or 0.09),
- $T$ is the number of days the loan is outstanding (180),
- and 360 is used instead of 365 in banking to simplify calculations.
Plugging in the numbers, the interest earned over 180 days is \$450. This interest is added to the original principal to find the maturity value—the total amount due when the note reaches the end of its term.
Thus, the maturity value is:
$$
\$10,000 + \$450 = \$10,450
$$
This makes Option A the correct answer. Understanding how to compute the maturity value is critical for both borrowers and lenders to plan cash flows and assess the cost of borrowing.