{"id":"cb_question_bank:e19efa51-d808-428e-85da-10218c337977","source_id":"cb_question_bank","source_item_id":"e19efa51-d808-428e-85da-10218c337977","external_id":null,"ibn":"11107-DC","question_id":"af142f8d","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.D.","skill":"Two-variable data: Models and scatterplots","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?","stimulus":"Amount invested Balance increase Account A $500 6% annual interest Account B $1,000 $25 per year","stimulus_html":"
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\n \n
\n \n \n \n \n \n \n \n \n \n
Amount investedBalance increase
Account A   $5006% annual interest
Account B$1,000$25 per year
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\n","stem_html":"

Two investments were made as shown in the table above. The interest in Account A is compounded once per year. Which of the following is true about the investments?

\n","rationale_html":"

Choice A is correct. Account A starts with $500 and earns interest at 6% per year, so in the first year Account A earns (500)(0.06) = $30, which is greater than the $25 that Account B earns that year. Compounding interest can be modeled by an increasing exponential function, so each year Account A will earn more money than it did the previous year. Therefore, each year Account A earns at least $30 in interest. Since Account B always earns $25 each year, Account A always earns more money per year than Account B.

Choices B and D are incorrect. Account A earns $30 in the first year, which is greater than the $25 Account B earns in the first year. Therefore, neither the statement that Account A always earns less money per year than Account B nor the statement that Account A earns less money than Account B at first can be true. Choice C is incorrect. Since compounding interest can be modeled by an increasing exponential function, each year Account A will earn more money than it did the previous year. Therefore, Account A always earns at least $30 per year, which is more than the $25 per year that Account B earns.

\n","correct_answer":["A"],"has_media":false,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.638000+00:00","source_updated_at":"2023-08-02T20:25:59.638000+00:00","options":[{"label":"A","content_html":"

Account A always earns more money per year than Account B.

\n","ord":0},{"label":"B","content_html":"

Account A always earns less money per year than Account B.

\n","ord":1},{"label":"C","content_html":"

Account A earns more money per year than Account B at first but eventually earns less money per year.

\n","ord":2},{"label":"D","content_html":"

Account A earns less money per year than Account B at first but eventually earns more money per year.

\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}