计算复利增长，了解时间和利率对投资收益的影响
复利是指在计算利息时，不仅对本金计算利息，还对之前产生的利息计算利息，即"利滚利"。复利是投资理财中最强大的力量之一，被爱因斯坦称为"世界第八大奇迹"。使用本复利计算器，您可以快速了解不同参数下投资收益的增长情况。
使用步骤：
Compound interest means calculating interest not only on the principal but also on previously earned interest — often called "interest on interest." Compound interest is one of the most powerful forces in investing, famously described by Einstein as "the eighth wonder of the world." Use this compound interest calculator to quickly see how your investments grow under different parameters.
How to Use:
复利计算的核心公式如下：
其中各参数含义：
当存在每月追加投资时，最终金额还需加上每月定投的终值，其计算公式为普通年金终值公式：
其中 PMT 为每期追加投资金额。最终总额 = 初始本金复利终值 + 每月定投终值。
The core compound interest formula is:
Where each parameter means:
When monthly contributions are involved, the final amount also includes the future value of the contribution series, calculated using the ordinary annuity future value formula:
Where PMT is the periodic contribution amount. Total final amount = Future value of initial principal + Future value of contributions.
场景：小王初始投入 ¥10,000，每月追加投资 ¥1,000，年预期收益率 8%，投资期限 10 年，按月复利。
计算过程：
计算结果：
通过这个例子可以看到，坚持每月定投并充分利用复利效应，10 年累计收益可超过总投入本金的一半以上。时间越长，复利的威力越明显。
Scenario: John starts with $10,000, contributes $1,000 monthly, expects an 8% annual return, invests for 10 years, compounded monthly.
Parameters:
Results:
This example shows that by consistently contributing monthly and harnessing the power of compound interest, total earnings over 10 years can exceed half of the total principal invested. The longer the time horizon, the more dramatic the compounding effect becomes.
单利只对本金计算利息，每期利息相同；复利则对本金和已产生的利息一起计算利息，即"利滚利"。在相同利率和时间下，复利的最终收益远高于单利，且时间越长差距越大。例如，10 万元按年利率 8% 投资 20 年，单利终值为 26 万元，而复利终值约 46.6 万元，相差近一倍。
Simple interest is calculated only on the principal, so each period earns the same amount of interest. Compound interest is calculated on both the principal and accumulated interest — "interest on interest." Under the same rate and time period, compound interest produces significantly higher returns than simple interest, and the gap widens over time. For example, investing $100,000 at 8% annual rate for 20 years yields $260,000 with simple interest but approximately $466,000 with compound interest — nearly double.
复利频率越高（如按日复利对比按年复利），最终收益会略高。这是因为更频繁的复利使利息更早开始产生新的利息。但实际差异通常不大——例如 8% 年利率投资 10 年，按年复利与按日复利的差异不到 1%。选择复利频率时，应根据实际投资产品的计息方式来选择。
The higher the compounding frequency (e.g., daily vs. annually), the slightly higher the final return, because more frequent compounding allows interest to start earning interest sooner. However, the actual difference is usually small — for example, at 8% annual rate over 10 years, the difference between annual and daily compounding is less than 1%. When selecting compounding frequency, match it to how your actual investment product calculates interest.
许多投资方式都能享受复利效应：银行存款（将利息转存）、基金定投（红利再投资）、债券（利息再投资）、股票（分红再投入）等。关键在于将获得的收益重新投入，而不是取出消费。此外，指数基金和 ETF 因其长期稳定的增长特性，非常适合利用复利效应实现财富增值。
Many investment methods can harness compound interest: bank deposits (rolling over interest), fund regular investments (reinvesting dividends), bonds (reinvesting coupon payments), and stocks (reinvesting dividends). The key is to reinvest the returns rather than withdrawing and spending them. Additionally, index funds and ETFs, with their long-term steady growth characteristics, are well-suited for leveraging compound interest to build wealth over time.
提高复利投资收益的关键策略包括：（1）尽早开始投资——时间是复利最好的朋友，越早开始，复利效应越显著；（2）坚持定期投入——每月定额投资可以平摊成本、降低风险；（3）选择合理的收益率——不要盲目追求高收益，应结合自身风险承受能力；（4）长期持有不中断——频繁买卖会增加交易成本并打断复利积累；（5）将收益再投资——确保所有利息和分红都重新投入，而非取出使用。
Key strategies to maximize compound interest returns: (1) Start early — time is compound interest's best friend; the earlier you start, the more dramatic the compounding effect. (2) Invest consistently — regular monthly contributions average out costs and reduce risk. (3) Choose reasonable return expectations — don't blindly chase high returns; align with your risk tolerance. (4) Hold long-term without interruption — frequent trading increases costs and breaks the compounding cycle. (5) Reinvest all returns — ensure all interest and dividends are reinvested rather than withdrawn for spending.