2. 外语
  3. A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for

A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for

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问题 A college student expects to earn at least $1,000 in interest on an initial investment of $20,000. If the money is invested for one year at interest compounded quarterly, what is the least annual interest rate that would achieve the goal?
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答案4.91 percent
解析 According to the formula for r percent annual interest, compounded quarterly, the value of the investment after 1 year is

By setting this value greater than or equal to $21,000 and solving for r, we get

We can use the fact that taking the positive fourth root of each side of an inequality preserves the direction of the inequality. This is also true for the positive square root or any other positive root.

To compute the fourth root, we can use the fact thatfor x ≥ 0; that is, we can compute a fourth root by taking a square root twice:

So the least annual interest rate is approximately 4.91 percent.
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