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.

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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

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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

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Assets & Dependencies

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

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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