题目

A deposit of $1,000 is made in a bank account, compounded annually, at a rate of r percent.

The amount accumulated after two years is greater than $1,210.

Quantity A

r

Quantity B

10%

选项

A.

Quantity A is greater.


B.

Quantity B is greater.


C.

The two quantities are equal.


D.

The relationship cannot be determined from the information given.


解析

本金为\(P\)、每期复利一次、利率为\(r\%\)、期数为\(t\)的本息和公式为: 本息和 = P × (1 + r/100)^t 代入数值, 1210 < 1000 × (1 + r/100)^2 1.21 < (1 + r/100)^2 1.1 < (1 + r/100) 或 -1.1 > (1 + r/100)(平方根不等式) 0.1 < r/100 或 -2.1 > r/100(因利率不能为负,舍去该不等式) 10 < r 因此,r > 10%,故选选项A
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