A company receives a 10%, 120-day note for $1,500. The total interest due on the maturity date is:
A. $50.00.
B. $150.00.
C. $75.00.
D. $37.50.
E. $87.50.
The correct answer and explanation is :
To calculate the total interest due on a note, we use the formula for simple interest:
$$
\text{Interest} = \text{Principal} \times \text{Rate} \times \frac{\text{Time}}{360}
$$
Given:
- Principal = \$1,500
- Annual Interest Rate = 10% = 0.10
- Time = 120 days
- Financial institutions often use a 360-day year for interest calculations.
Step-by-step Calculation:
$$
\text{Interest} = 1500 \times 0.10 \times \frac{120}{360}
$$
$$
\text{Interest} = 1500 \times 0.10 \times 0.3333
$$
$$
\text{Interest} = 1500 \times 0.03333 = 50.00
$$
Correct Answer:
A. \$50.00
Explanation:
When a company receives a promissory note, it is agreeing to be paid a certain amount (called the principal) plus interest after a specified period. In this case, the note has a face value (principal) of \$1,500 and carries a 10% annual interest rate for 120 days.
The simple interest formula is used because this is a short-term note and it does not compound. The 360-day year convention (also known as a banker’s year) simplifies interest calculations in financial contexts. Rather than using 365 days, using 360 allows easier computation and is a standard practice.
The 120-day period is one-third of a 360-day year. So, only one-third of the annual interest (10%) is earned. That’s:
$$
10\% \div 3 = 3.33\%
$$
Then, 3.33% of \$1,500 is:
$$
0.03333 \times 1500 = 50
$$
Thus, when the note matures in 120 days, the total interest due will be \$50.00, making that the correct and accurate answer.