The garden is semi-circular with a radius $r = 420$ m. The perimeter of a semi-circular garden consists of the length of the semi-circular arc and the length of the diameter. Length of the semi-circular arc $= \frac{1}{2} (2\pi r) = \pi r$. Length of the diameter $= 2r$. Total perimeter for one round of fencing $= \pi r + 2r = r(\pi + 2)$. Using the approximation $\pi = \frac{22}{7}$: Perimeter $= 420 \left(\frac{22}{7} + 2\right)$ Perimeter $= 420 \left(\frac{22}{7} + \frac{14}{7}\right)$ Perimeter $= 420 \left(\frac{22+14}{7}\right)$ Perimeter $= 420 \left(\frac{36}{7}\right)$ Perimeter $= (60 \times 7) \times \frac{36}{7}$ Perimeter $= 60 \times 36 = 2160$ m. The garden is to be fenced with five rounds of wire. Total length of wire needed $= 5 \times \text{Perimeter for one round}$ Total length of wire needed $= 5 \times 2160 \text{ m} = 10800 \text{ m}$. The cost of the wire is Rs. $60$ per metre. Total cost of the wire $= \text{Total length of wire} \times \text{Cost per metre}$ Total cost $= 10800 \text{ m} \times \text{Rs. } 60/\text{m}$ Total cost $= \text{Rs. } 648000$. Therefore, the cost of the wire needed for fencing is Rs. $6,48,000$.