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Compound Interest — Exponential Growth

対象: High Schoolカテゴリ: Economics

説明

Demonstrates the power of compound interest by comparing three growth scenarios over 30 years: no interest (flat), simple interest at 5% (linear), and compound interest at 5% (exponential). Illustrates the compounding formula and a concrete $1000 @ 7% example showing $7,612 after 30 years.

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Compound Interest — Exponential Growth

Description

Demonstrates the power of compound interest by comparing three growth scenarios over 30 years: no interest (flat), simple interest at 5% (linear), and compound interest at 5% (exponential). Illustrates the compounding formula and a concrete $1000 @ 7% example showing $7,612 after 30 years.

Phases

# Phase Name Duration Description
1 Title & Formula 6s Show title and the compound interest formula A = P(1 + r/n)^(nt)
2 Axes Setup 4s Draw axes: X = Years (0-30), Y = Balance ($)
3 Draw Curves 10s Animate three curves drawing simultaneously: flat, linear, exponential
4 Label Curves 5s Label each curve with color-coded text
5 Highlight Gap 6s Show vertical arrow indicating the growing gap between compound and simple at year 30
6 Numerical Example 8s Display $1,000 at 7% for 30 years = $7,612 with breakdown
7 Rule of 72 6s Introduce Rule of 72: years to double = 72 / interest rate

Layout

+-----------------------------------------------+
|     Compound Interest — Exponential Growth     |
|  Balance ($)                                   |
|  ^                               ___/ Compound |
|  |                          ____/              |
|  |                     ____/   /               |
|  |              ______/  Simple                |
|  |   ___________                               |
|  |  No Interest (flat)                         |
|  +-----------------------------------> Years   |
|     0        10        20        30            |
|  A = P(1 + r/n)^(nt)                          |
|  $1,000 @ 7% for 30 yrs = $7,612              |
+-----------------------------------------------+

Area Descriptions

  • Top: Title text
  • Center: Axes with three plotted curves
  • Bottom-left: Formula MathTex
  • Bottom-right: Numerical example callout

Assets & Dependencies

  • Fonts: LaTeX / sans-serif
  • Manim version: ManimCE 0.19.1

Notes

  • Flat line: gray/white
  • Simple interest: blue straight line
  • Compound interest: gold/green exponential curve
  • Axes use dollar amounts (0 to ~8000) on Y and years (0-30) on X
  • Background: dark navy #1a1a2e
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