With credit terms of 2/10, n/30, the annual interest rate for paying in 10 days instead of 30 days is closest to

With credit terms of 2/10, n/30, the annual interest rate for paying in 10 days instead of 30 days is closest to:

A. 2%

B. 24%

C. 30%

D. 36%

The Correct Answer and Explanation is :

Correct Answer: D. 36%

Explanation:

The credit terms 2/10, n/30 mean that the buyer receives a 2% discount if payment is made within 10 days; otherwise, the full invoice amount is due in 30 days. To determine the annual interest rate implied by delaying payment beyond the discount period, we use the effective interest rate formula: \text{Effective Rate} = \left( \frac{\text{Discount %}}{100\% – \text{Discount %}} \right) \times \frac{365}{\text{Extra Days of Credit}}

Step-by-step calculation:

1. Discount Offered:2%
   • This means that the buyer can either pay 98% of the invoice within 10 days or 100% at 30 days.
2. Opportunity Cost:
   • If the buyer forgoes the discount, they are essentially borrowing the remaining 2% of the invoice for an additional 20 days (30 – 10).
3. Formula Application: Effective Rate=(298)×36520\text{Effective Rate} = \left( \frac{2}{98} \right) \times \frac{365}{20}
4. Solving for Effective Annual Interest Rate: (298)=0.02041\left( \frac{2}{98} \right) = 0.02041 0.02041×36520=0.37270.02041 \times \frac{365}{20} = 0.3727 0.3727×100=37.27%0.3727 \times 100 = 37.27\%

Conclusion:

The annual interest rate for delaying payment beyond the 10-day discount period is approximately 36%, making the correct answer D. 36%.

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