Calculating short position cash flows and returns. Assume that an investor short$-$sells $500$ shares of stock at a price of $$85$ a share, making a $50$ percent margin deposit. A year later, she repurchases the borrowed shares at $$50$ a share.

a$.$ How much of her money did the short$-$seller have to put up to make this transaction?

b$.$ How much money did the investor make, or lose, on this transaction?

c$.$ What rate of return did she make on her invested capital $($see part a$)?$