Question

If a company purchases merchandise on terms of 2/10, n/30, the cash discount available (assuming a 360-day year) is equivalent to an effective annual interest rate of

a. 2%
b. 24%
c. 36%
d. 60%

Answer 1

The effective annual interest rate equivalent for a cash discount of 2/10, n/30 is greater than 36%, which would make option (c) the correct answer.

Step-by-step explanation:

The student has asked about calculating the effective annual interest rate equivalent for cash discount terms of a merchandise purchase. When the terms are 2/10, n/30, it means the company can take a 2% discount if it pays within 10 days; otherwise, the full amount is due in 30 days. To determine the annualized rate, first consider the opportunity cost of not taking the discount, which is 2% for the 20-day period (30-10 days). To annualize, we use the formula for the effective annual rate (EAR) which is (1+rate/n)^n - 1, where 'rate' is the discount rate not taken, and 'n' is the number of times the discount period fits into a 360-day year. Since there are approximately 18 periods of 20 days in a 360-day year, we can calculate the EAR as (1 + 0.02/0.98)^18 - 1, leading to an EAR greater than 36%, which matches option c. 36%.