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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?
Account A always earns more money per year than Account B.
Account A always earns less money per year than Account B.
Account A earns more money per year than Account B at first but eventually earns less money per year.
Account A earns less money per year than Account B at first but eventually earns more money per year.
Amount invested Balance increase Account A $500 6% annual interest Account B $1,000 $25 per year
Hard-difficulty · SAT Math · Nonlinear Functions — Exponential growth and decay functions. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
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.
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