How the Dividend Doubling Formula Works
When you reinvest dividends at an after-tax yield `y` and the company raises its dividend per share at an annual rate `g`, your combined income growth rate `R` is:
Combined Growth Rate (R) = (1 + y) × (1 + g) - 1From that combined rate `R`, you can find your doubling time in two ways:
Rule of 72 Estimate (Years) = 72 ÷ (R × 100)
Exact Doubling Time (Years) = ln(2) ÷ ln(1 + R)Worked Example: 3.5% Yield + 7.0% Annual Dividend Growth
Suppose you hold a dividend growth ETF inside a Roth IRA (`0%` tax) that pays a **3.50% dividend yield** (`y = 0.035`) and raises its dividend by **7.00% per year** (`g = 0.07`):
- Without DRIP (Cash Taken): Your income only grows at `7.00%` per year. Using `ln(2) ÷ ln(1.07)`, your dividend income doubles every **10.24 years**.
- With DRIP Enabled: Your combined rate is `(1.035 × 1.07) - 1 = 10.745%` per year. Using `ln(2) ÷ ln(1.10745)`, your dividend income doubles every **6.79 years**.
Turning on DRIP cuts your doubling time by **3.45 years**. To calculate a stock’s past growth rate from its dividend history, use our dividend growth rate calculator.
Years to Double Your Dividend Income (2x, 4x, and 8x)
Here is how many years it takes to reach `2x`, `4x`, and `8x` your starting dividend income across different combined growth rates:
| Combined Rate (Yield + Growth) | Rule of 72 (2x) | Exact Years to 2x | Exact Years to 4x | Exact Years to 8x |
|---|---|---|---|---|
| 5.0% / yr | 14.40 yrs | 14.21 yrs | 28.41 yrs | 42.62 yrs |
| 7.0% / yr | 10.29 yrs | 10.24 yrs | 20.49 yrs | 30.73 yrs |
| 9.0% / yr | 8.00 yrs | 8.04 yrs | 16.09 yrs | 24.13 yrs |
| 11.0% / yr | 6.55 yrs | 6.64 yrs | 13.28 yrs | 19.93 yrs |
| 12.0% / yr | 6.00 yrs | 6.12 yrs | 12.23 yrs | 18.35 yrs |
Common Mistakes When Using the Rule of 72
- Forgetting taxes on the DRIP yield portion: In a taxable account, a `15%` tax reduces a `4.0%` DRIP yield to `3.4%`. Taxes do not reduce the company’s annual dividend growth rate `g`, only the new shares you buy with each payout.
- Assuming rapid share price spikes help DRIP: If a stock’s price jumps faster than its dividend, its current yield drops, which means each reinvested dividend buys fewer shares. Test rising share prices in our full DRIP calculator.
- Using the Rule of 72 for huge growth rates: Above 15% or 20% annual growth, the Rule of 72 becomes slightly less accurate than the exact `ln(2) ÷ ln(1 + R)` formula shown in our tool.