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I’m confused about when to use the Effective Annual Rate (EAR) versus the Simple Annual Rate when calculating annual percentage cost. In the study hub question, it seems the calculation uses a simple annual rate to determine the cost of rejecting a discount. The working states that because the question does not ask for EAR, a simple annual rate is used. I’m unsure whether this approach is always valid or if there’s a specific rule to follow. Kindly find the reference below:
5. Scrimpy Co buys materials from Frugal Enterprises. Frugal offers discount terms of 2% discount for payment within 10 days or full payment within 30 days.
Assuming a 360-day year, what is the annual percentage cost associated with Scrimpy’s failure to take advantage of the discount offered by Frugal?
A.2.0%
B.33.3%
C.36.0%
D.36.7%The correct answer is D.
WORKING
If Scrimpy rejects the discount it costs $2 to borrow $98 from the supplier for an extra 20 days. Hence 20-day cost of rejecting discount is 2/98 = 2.04%. As the requirement does not ask for an effective annual rate, a simple annual rate can be calculated as 36.7% (2.04% × 360/20).
When calculating the cost of rejecting a discount, as in the case of Scrimpy Co, the Simple Annual Rate can be used effectively. The calculation involves determining the cost of not taking the discount over the period it is offered, and since the question does not specify the need for an EAR, the Simple Annual Rate is a valid approach.
It is important to note that using the EAR can provide a more accurate representation of the cost when compounding is involved. The choice between the two methods may lead to different results, and compounding typically results in a higher effective rate, but if the question does not specify the use of EAR, it is generally acceptable to use the Simple Annual Rate.m
Now let’s take the same scenario, and assume that the overdraft rate is 40%.
We are asked to decide whether to take the discount or not.Rationally, one should use the EAR rather than the Simple Annual Rate for the comparison, right?
Or, since it is not explicitly mentioned to apply the EAR, one should opt for the Simple Annual Rate instead?So where the overdraft rate is 40%, you should consider using the Effective Annual Rate for comparison, especially since that accounts for the effects of compounding, which can provide a more accurate representation of the cost of not taking the discount.
But remember, if the question does not explicitly mention the need to apply the Effective Annual Rate using the Simple Annual Rate can still be acceptable in the question. The key is to ensure that the chosen method aligns with the context of the question. If it’s not clear I would say either would be acceptable if it is clear then ATQ set..
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