Compound Interest Calculator
See how a starting sum and regular contributions grow at a given annual return. Includes a year-by-year breakdown table and an inline growth curve.
Enter a starting amount, a recurring contribution, how often you contribute, an annual return, and a time horizon. The calculator shows how your money compounds year by year.填入初始金额、定期投入、投入频率、年化收益率和时间跨度。计算器将逐年展示你的资金如何复利增长。
Fill in all fields to see how your money grows.填入所有字段即可查看资金增长情况。
- Total contributed合计投入
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- Growth (interest)增长（利息）
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- Growth multiple增长倍数
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Compound growth means your returns earn returns. The longer the horizon and the higher the rate, the more dominant the compounding effect becomes — a dollar of growth today adds to the base that all future periods compound on top of.复利增长意味着你的收益也在产生收益。时间跨度越长、收益率越高，复利效应就越显著——今天的一美元增长，成为未来所有周期继续复利的基础。
01The formula公式
where i = annual rate ÷ 100 ÷ frequency, m = years × frequency其中 i = 年利率 ÷ 100 ÷ 频率，m = 年数 × 频率
(Ordinary annuity — contributions at the end of each period)（普通年金——每期末投入）
The "ordinary annuity" convention matters: contributions land at the end of each period, not the start. The first period's contribution earns one fewer period of interest than the principal. If your contributions go in at the start of each period (annuity-due), the future value would be slightly higher — but this convention is the standard baseline."普通年金"约定很重要：投入发生在每期末，而非期初。第一期的投入比本金少计一期利息。如果你在每期初投入（期初年金），终值会略高——但普通年金是标准基准。
02A worked example一个算例
Suppose you start with $10,000, add $500 every month, earn 7% per year, and let it run for 10 years.假设你以 $10,000 起始，每月追加 $500，年收益率 7%，持续 10年。
- Monthly rate i = 7% ÷ 12 ≈ 0.5833%月利率 i = 7% ÷ 12 ≈ 0.5833%
- Number of periods m = 10 × 12 = 120期数 m = 10 × 12 = 120
- FV ≈ $106,639终值 ≈ $106,639
- Total contributed = $10,000 + 500 × 120 = $70,000合计投入 = $10,000 + 500 × 120 = $70,000
- Growth (interest) ≈ $36,639 — over half of contributed, earned for free by staying invested.增长（利息）≈ $36,639——超过投入的一半，靠长期持有白得的回报。
03The common trap常见陷阱
A 50% gain followed by a 50% loss is not a 0% net result — it's −25%. Compounding is multiplicative: 1.5 × 0.5 = 0.75. When you read "average annual return of X%", check whether it's an arithmetic average (often quoted, optimistic) or a geometric average (compound annual growth rate — what money actually does). The CAGR is always lower than or equal to the arithmetic mean.上涨50%再下跌50%，净结果不是0%，而是−25%。复利是乘法：1.5 × 0.5 = 0.75。当你看到"年均收益率X%"时，要确认这是算术平均（常被引用，偏乐观）还是几何平均（即CAGR——资金实际经历的）。CAGR始终低于或等于算术均值。
04Where this breaks它的局限
- The rate is assumed constant. Real returns are volatile. Sequence of returns matters: a bad year early, when the balance is smaller, hurts less than a bad year late, when there's more to lose.收益率假设固定不变。实际回报率是波动的。回报顺序很重要：早期亏损时余额小影响较小，晚期亏损时本金已积累更多则伤害更大。
- Taxes and inflation are not modeled. After-tax and inflation-adjusted returns can differ materially from the nominal figure used here.未计入税收和通胀。税后、通胀调整后的实际回报率与这里使用的名义数字可能相差很大。
- Contributions are assumed uniform. Real savings rates vary. Gaps in contributions reduce FV proportionally.假设投入金额不变。实际储蓄率会变化。中断投入会按比例降低终值。
Time is the most powerful input. Doubling your rate is hard; doubling your years is often possible.时间是最强大的变量。将收益率翻倍很难；将年数翻倍往往是可能的。
See how compounding interacts with drawdowns in Why a 50% loss needs a 100% gain, and explore growth rates with the 在 为什么亏损50%需要盈利100%才能回本 中了解复利与回撤的关系，或用 CAGR calculatorCAGR计算器. For long-run thinking, Compound growth for traders is the companion piece.探索增长率。长期思维的配套阅读：交易者的复利增长。