If cash is borrowed on a $55,800, 9-month, 10% note on August 1, how much interest expense would be incurred by December 31?
The correct answer and explanation is :
To calculate the interest expense incurred by December 31 on a \$55,800, 9-month, 10% note borrowed on August 1, we need to use the formula for simple interest:
Interest Formula:
$$
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
$$
- Principal (P): \$55,800
- Rate (R): 10% annually = 0.10
- Time (T): From August 1 to December 31 is 5 months out of 12 = $\frac{5}{12}$ year
$$
\text{Interest} = 55,800 \times 0.10 \times \frac{5}{12}
$$
$$
\text{Interest} = 55,800 \times 0.10 \times 0.4167 = 55,800 \times 0.04167 \approx \boxed{2,325.09}
$$
✅ Correct Answer: \$2,325.09
📘 Explanation (Approx. 300 Words):
When a company borrows money using a note payable, interest typically accrues over time and is recognized as an expense as it is incurred. In this case, the company borrowed \$55,800 on August 1 under the terms of a 9-month, 10% annual interest note. Although the full term of the note spans 9 months, the company must report how much interest expense it has incurred by the end of the accounting period, which is December 31.
To calculate how much interest has accrued by December 31, you first identify how many months have passed since the note was issued. From August 1 to December 31, there are 5 months (August, September, October, November, and December).
Because the interest rate is annual (10%), you must convert the time to a fraction of the year: 5/12. Using the simple interest formula:
$$
\text{Interest} = \text{Principal} \times \text{Rate} \times \text{Time}
$$
you plug in:
$$
55,800 \times 0.10 \times \frac{5}{12} = 2,325.09
$$
This amount represents the interest expense that must be recorded on the income statement as of December 31. It’s also included as an accrued liability (interest payable) on the balance sheet if the note hasn’t been paid yet. The remaining interest for the note’s total 9-month term will continue accruing into the next accounting period.