Compound Growth Calculator Formula
Understand the math behind the compound growth calculator. Each variable explained with a worked example.
Formulas Used
Final Val
final_val = initial * pow(1 + rate / 100, periods)Total Gain
total_gain = initial * pow(1 + rate / 100, periods) - initialMultiplier
multiplier = pow(1 + rate / 100, periods)Doubling Time
doubling_time = rate > 0 ? 72 / rate : 0Variables
| Variable | Description | Default |
|---|---|---|
initial | Initial Value | 1000 |
rate | Growth Rate (%)(%) | 5 |
periods | Number of Periods | 10 |
How It Works
Compound Growth
Formula
Final = Initial × (1 + r)^n
where r is the growth rate per period and n is the number of periods.
Rule of 72
To estimate doubling time: Periods ≈ 72 / rate(%)
At 6% growth, doubling takes approximately 72/6 = 12 periods.
Worked Example
1000 growing at 5% per year for 10 years.
- 01Final = 1000 × (1.05)^10
- 02= 1000 × 1.6289
- 03= 1628.89
- 04Total gain = 628.89
- 05Doubling time ≈ 72/5 = 14.4 years
Frequently Asked Questions
What is compound growth?
Compound growth means that growth applies not just to the original amount, but also to all previously accumulated growth. Each period's gain builds on the previous total.
What is the Rule of 72?
The Rule of 72 is a quick way to estimate doubling time: divide 72 by the growth rate percentage. At 8% growth, doubling takes about 72/8 = 9 periods.
How does compound growth differ from simple growth?
Simple growth applies the rate to the original amount each period (linear). Compound growth applies it to the current total (exponential), so it accelerates over time.
Learn More
Guide
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