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.
Explanation
Correct answer: A.
Choice A is correct. Account A starts with $ and earns interest at per year, so in the first year Account A earns $, which is greater than the $ 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 $ in interest. Since Account B always earns $ each year, Account A always earns more money per year than Account B.
Desmos solution:
Note: Account A starts by earning ＄30 annually, above Account B's ＄25, and compounding makes Account A's yearly interest increase.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice B
Choice B is incorrect. Account A earns $ in the first year, which is greater than the $ Account B earns in the first year. Therefore, the statement that Account A always earns less money per year than Account B cannot be true.
Choice C
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 $ per year, which is more than the $ per year that Account B earns.
Choice D
Choice D is incorrect. Account A earns $ in the first year, which is greater than the $ Account B earns in the first year. Therefore, the statement that Account A earns less money than Account B at first cannot be true.