If a company purchases merchandise on terms of 1/10, n/30, the cash discount available is equivalent to what effective annual rate of interest (assuming a 360-day year)?

Question

Quizplus · Accepted Answer

The terms 1/10, n/30 mean that the company can take a cash discount of 1% if they pay within 10 days, or pay the full amount within 30 days. 
To find the effective annual rate of interest, we need to calculate the cost of not taking the discount and paying after 10 days. 
The formula for effective annual rate is:

(1 + i)^n = (1 - d/p)^m

where:
i = the effective annual rate
n = the number of times the discount period occurs in a year (360/10 = 36)
d = the discount rate (1%)
p = the percentage paid if the discount is not taken (100% - 1% = 99%)
m = the number of times the discount period doesn't occur in a year (360/30 - 12)

Plugging in the values, we get:

(1 + i)^36 = (1 - 1/99)^12
(1 + i)^36 = 0.8885
1 + i = (0.8885)^(1/36)
1 + i = 0.998769
i = 0.998769 - 1
i = -0.001231 or -0.1231%

Since the effective annual rate is negative, this means that taking the cash discount is actually a better deal than any loan or financing option available.

Therefore, the answer is C) 18%.

If a Company Purchases Merchandise on Terms of 1/10, N/30