您有 20,000 美元，希望将其投资于未来。如果您将其存入银行，以 5% 的利率投资 3 年，每月复利，您将拥有多少钱（四舍五入到最接近的美元）？

Question

BlackTom AI · Accepted Answer

这道题给出的信息是：本金 $20,000，年利率 5%，期限 3 年，按月复利。
由于题干要求四舍五入到最近的美元，我们需要使用月度复利公式：FV = P × (1 + r/12)^(12t)，其中 P 是本金，r 是年利率，t 是年数。
把数值代入：P = 20,000；r/12 = 0.05/12 = 0.0041666667；12t = 12×3 = 36，因此 FV = 20,000 × (1.0041666667)^36。
接下来估算或逐步计算指数部分：(1.0041666667)^36 近似等于 exp(36 × ln(1.0041666667))。
先估算 ln(1.0041666667) ≈ 0.004158（这是一个对小数的自然对数近似），于是 36 × 0.004158 ≈ 0.1497。
再取指数：exp(0.1497) ≈ 1.1616。
因此 FV ≈ 20,000 × 1.1616 ≈ 23,232。
最终的近似值在四舍五入到整美元时大约是 $23,232。
注意事项：在某些精确计算中，结果可能略有不同，取决于逐步取值的舍入方式，但通常会落在接近 $23,230–$23,235 的区间内。
另外，题目提供的答案选项列表为空，无法逐项分析选项的正确性与错误之处。如果有具体的选项，我可以逐条解析每个选项的正确性及常见误解。

PMGT2850（无铅）测验 1 的练习测试

您有 20,000 美元，希望将其投资于未来。如果您将其存入银行，以 5% 的利率投资 3 年，每月复利，您将拥有多少钱（四舍五入到最接近的美元）？

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PMGT2850（无铅） 测验 1 的练习测试

您有 20,000 美元，希望将其投资于未来。如果您将其存入银行，以 5% 的利率投资 3 年，每月复利，您将拥有多少钱（四舍五入到最接近的美元）？

查看解析

登录即可查看完整答案

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Part 1Consider a twominus−year ​investment: Given a constant and positive interest​ rate, the interest earned in the second year will be greater than the interest earned in the first year​ (assuming annual​ compounding). Part 1 True False

If Jack and Jill deposit $1,000 into a savings account that earns 4.5% annual interest (compounded monthly), how long will it take for their money to double to $2,000?

How much will you get back on a five year investment of $100 that pays 5% interest per year?

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If you deposit $10,000 in an account with an annual rate of 9% compounded semiannually, how long will it take for you to have $2,000,000 in the account?

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