# 复利与指数增长

交互式复利、72法则与指数增长惊人力量的可视化

> 标准页面: https://elysiatools.com/zh/visualizations/compound-interest

- **分类:** Math

## 概述

Interactive visualization of compound interest, the Rule of 72, and the surprising power of exponential growth. Compare compound vs simple vs linear growth side-by-side with adjustable parameters: principal P ($100-$1M), annual rate r (0.1%-30%), years t (1-80), compounding frequency (annual/quarterly/monthly/daily/continuous), and optional monthly contributions. Four synchronized views: (1) Growth curves showing compound, simple interest, and linear trajectories with doubling markers; (2) Interest gap chart highlighting the accelerating difference between compound and simple interest; (3) Logarithmic scale view revealing exponential growth as a straight line; (4) Stacked area wealth breakdown separating contributions from earned interest. The Rule of 72 panel shows approximate vs exact doubling time with error percentage. Statistics track final values, multiplier, number of doublings, and gap vs simple interest. Education covers the compound interest formula, the Rule of 72 derivation and accuracy, why exponential growth is counterintuitive (lily pond puzzle), retirement savings (early bird advantage), credit card debt traps, inflation as hidden tax, exponential growth bias (Stango & Zinman 2009), present bias and discounting, and teaching exponential thinking through stories. 8 languages (zh, en, es, fr, de, ru, pt, ja).

## 相关内容

- [零级反应 - Zero-Order Reaction](https://elysiatools.com/zh/visualizations/zero-order-reaction): 零级反应动力学和浓度随时间变化的交互式可视化
- [一级反应 - First-Order Reaction](https://elysiatools.com/zh/visualizations/first-order-reaction): 一级反应动力学和指数浓度衰减的交互式可视化
- [二级反应 - Second-Order Reaction](https://elysiatools.com/zh/visualizations/second-order-reaction): 二级反应动力学和双分子碰撞动力学的交互式可视化
- [阿伦尼乌斯方程 - Arrhenius Equation](https://elysiatools.com/zh/visualizations/arrhenius-equation): 温度对反应速率影响的交互式可视化 - 探索活化能、指数因子和速率常数的关系
- [可逆反应 - Reversible Reaction](https://elysiatools.com/zh/visualizations/reversible-reaction): A ⇌ B 可逆反应动力学的交互式可视化 - 探索正逆反应速率、平衡常数和浓度随时间的变化
- [连续反应 - Consecutive Reaction](https://elysiatools.com/zh/visualizations/consecutive-reaction): A → B → C 连续反应动力学的交互式可视化 - 探索中间物浓度峰值、决速步和所有物种的完整演化
- [链式反应 - Chain Reaction](https://elysiatools.com/zh/visualizations/chain-reaction): 自由基链式反应聚合的交互式可视化 - 探索引发、增长、终止步骤，链增长动画和分子量分布
- [勒夏特列原理 - Le Chatelier's Principle](https://elysiatools.com/zh/visualizations/le-chateliers-principle): 勒夏特列原理的交互式可视化 - 探索浓度、压强和温度变化如何影响化学平衡，配合分子动力学动画展示平衡移动过程