{"id":"aqua_rat:b41587c5ca3d1964693791b7a90d9442","source_id":"aqua_rat","source_item_id":"b41587c5ca3d1964693791b7a90d9442","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"A merchant receives an invoice for a motor boat for $20 000 with terms 4/30, n/100. What is the highest simple interest rate at which he can afford to borrow money in order to take advantage of the discount?","stimulus":"","stimulus_html":null,"stem_html":"<p>A merchant receives an invoice for a motor boat for $20 000 with terms 4/30, n/100. What is the highest simple interest rate at which he can afford to borrow money in order to take advantage of the discount?</p>","rationale_html":"<p>Suppose the merchant will take advantage of the cash discount of 4% of $20 000 = $800 by paying the bill within 30 days from the date of invoice. He needs to borrow $20 000 = $800 = $19 200. He would borrow this money on day 30 and repay it on day 100 (the day the original invoice is due) resulting in a 70-day loan. The interest he should be willing to pay on borrowed money should not exceed the cash discount $800.</p><p>r=I/pt=21.73%</p><p>The highest simple interest rate at which the merchant can afford to borrow money is 21.73%. This is a break-even rate. If he can borrow money, say at a rate of 15%, he should do so. He would borrow $19 200 for 70 days at 15%. Maturity value of the loan is $19 200(1+0.15(70/365))=$19 752.33</p><p>savings would be $20 000 − $19 752.33 = $247.67</p><p>A</p>","correct_answer":["A"],"equiv_key":"05f14610dd118386fc2beb9d","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>247.67</p>","ord":0},{"label":"B","content_html":"<p>237.67</p>","ord":1},{"label":"C","content_html":"<p>227.67</p>","ord":2},{"label":"D","content_html":"<p>215.67</p>","ord":3},{"label":"E","content_html":"<p>None of these</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}