Compound Interest β Exponential Growth
Audience: High SchoolCategory: Economics
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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Compound Interest β 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 = $7,612 with breakdown |
| 7 | Rule of 72 | 6s | Introduce Rule of 72: years to double = 72 / interest rate |
Layout
+-----------------------------------------------+
| Compound Interest β Exponential Growth |
| Balance ($) |
| ^ ___/ 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