Thus, the smallest three-digit number divisible by both 9 and 12 is \(\boxed{108}\).A venture capitalist invests $500,000 in a clean technology startup that promises a 12% annual return compounded quarterly. If all returns are reinvested, how much will the investment be worth after 3 years?

["Thus, the smallest three-digit number divisible by both 9 and 12 is (\boxed{108}).", "---", "### How a Venture Capital Investment in Clean Tech Grows Over Time", "In the rapidly evolving world of clean technology, smart investments play a crucial role in driving innovation and sustainability. A compelling example is a venture capitalist who commits $500,000 to a promising clean tech startup offering a 12% annual return, compounded quarterly. Understanding how this investment grows over 3 years can inspire confidence in the potential returns from emerging green technologies.", "#### Understanding Compound Interest", "When returns are compounded quarterly, interest is calculated and added to the principal four times per year. This means you earn returns not just on your initial capital but also on the accumulated interest—accelerating growth over time.", "---", "### The Math Behind the Growth", "Given:\n- Principal ((P)) = $500,000\n- Annual interest rate ((r)) = 12% = 0.12\n- Compounding frequency ((n)) = 4 (quarterly)\n- Time ((t)) = 3 years", "The compound interest formula is:\n[\nA = P \left(1 + \frac{r}{n}\right)^{nt}\n]", "Plug in the values:\n- ( r/n = 0.12 / 4 = 0.03 )\n- ( nt = 4 \ imes 3 = 12 )", "[\nA = 500000 \left(1 + 0.03\right)^{12} = 500000 \ imes (1.03)^{12}\n]", "Using a calculator:\n[\n(1.03)^{12} \approx 1.42576\n]", "So:\n[\nA \approx 500000 \ imes 1.42576 = 712,880\n]", "---", "### Final Result", "After 3 years, with a 12% annual return compounded quarterly, the investment of $500,000 will grow to approximately:\n[\n\boxed{$712,880}\n]", "This demonstrates how early and strategic investments in clean tech—supported by compound growth—can yield substantial financial returns while advancing environmental progress."]