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.
选项
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