Answer (D) is correct . If the gross amount of the invoice is $1,000, the buyer will pay $970 [$1,000 × (1.0 – .03)] if (s)he takes the discount. If (s)he does not, (s)he will pay $30 for the use of $970 for up to an additional 35 days. The percentage cost of not taking the discount is the annualized interest rate, that is, the $30 cost divided by the $970 effectively ? borrowed for 35 days, multiplied by the number of 35-day periods in a 360-day year. Thus, the cost of forgoing the discount is 31.81% [($30 ÷ $970) × (360 ÷ 35)]. The annualized cost of not taking a discount is calculated with this formula: Cost of not taking discount = [3% ÷ (100% – 3%)] × [360 days ÷ (45 days – 10 days)] = (3% ÷ 97%) × (360 days ÷ 35 days) = 3.0928% × 10.29 = 31.81%
Answer (A) is incorrect because This percentage assumes payment of $20 to borrow $1,000 for 30 days.
Answer (B) is incorrect because This percentage assumes terms of 3/10, net 40.
Answer (C) is incorrect because This percentage assumes payment of $30 to borrow $1,000 for 30 days.
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