A retailer forecasts that its sales in the first month of $2011$ will be $$600,000$ and will then grow at $4\%$ per month for the next three months. It prices its products by adding a mark$-$up of $20\%$ to its purchase cost. The retailer always carries sufficient inventory to cover the next month's forecast sales.What is the forecast inventory $($to the nearest dollar$)$ at the end of the second month of $2011?$