To help the marketing department with next year's marketing activities planning, Sara collected some information that would help them prepare the budget. She learned, that only $2$ in $3$ loan applications are approved. Their social media advertising showed a very good result of a $5\%$ click$-$through rate for every impression on the social media advertisement. From those who clicked the advertisement, on average, $15\%$ would fill out the application form on the website. The bank is paying $$50$ per $100$ impressions on social media platforms. Marketing is expecting at least $250$ approved loans to come from social media channels.

How many leads $($applications$)$ social media platforms should generate to get the desired number of approved loans?