From December 6, 2025, to December 31, 2038, there are 4,793 days. This period spans 13 years
To calculate the continuous compound growth rate, use the formula:
$$
r = \frac{\ln\left(\frac{A}{P}\right)}{t}
$$
Where:
- $ A = 1,000,000,000 $ (final value)
- $ P = 100,000 $ (initial value)
- $ t = 13.07 $ years (from December 6, 2025, to December 31, 2038)
First, compute the ratio:
$$
\frac{A}{P} = \frac{1,000,000,000}{100,000} = 10,000
$$
Then:
$$
\ln(10,000) \approx 9.2103
$$
Now divide by time:
$$
r = \frac{9.2103}{13.07} \approx 0.7047
$$
So, the **continuous compound growth rate is approximately 70.47% per year**.
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