Three. (20 points) A company produces computers, and in 1997, the average production cost per unit was 5000 yuan, with a pure profit margin of 20% used to set the factory price. Starting from 1998, the company strengthened management and technological transformation, leading to a gradual reduction in production costs. By 2001, the factory price per computer was only 80% of the 1997 factory price, but the company achieved a 50% pure profit. Calculate the average annual reduction percentage in production costs from 1997 to 2001, based on the 1997 production cost (accurate to 0.01). (For calculations: $\sqrt{2}=1.414, \sqrt{3}=1.732, \sqrt{5}=2.236$.)
Three, the ex-factory price in 1997 is
$$
5000(1+20 \%)=6000 \text { (yuan). }
$$

Let the production cost per computer in 2001 be $x$ yuan. Then $x(1+50 \%)=6000 \times 80 \%$. Solving for $x$ gives $x=3200$ (yuan).
Let the annual reduction in production cost be $y$. Then
$$
(1-y)^{4} \times 5000=3200 \text {. }
$$

Solving for $y$ gives $y=1-\frac{2}{\sqrt{5}} \approx 1-\frac{2}{2.236} \approx 11 \%$.
Answer: Omitted.