As a savvy investor, you have decided all the hype about electric vehicles is legit. So you buy $100$ shares of Tesla stock for $$250\mathrm{.}08$ a share at the beginning of $2024.$ However, you know it is prudent to buy it on margin, so and you find a broker with a margin requirement of $65\%.$ Additionally, there is a commission rate of $2\%$ of the purchase or sale price, and an interest rate is $10\%$ on margin loans from this broker. Based on this information calculate the follow

a$.$ The commission cost for buying the stock on margin

b$.$ The Initial margin requirement and amount you will borrow for margin purchase

Today, you have decided to close out your Tesla position buy selling the stock at its current price of $$144\mathrm{.}33.$ However, while you held the stock, Tesla paid a dividend $($first time ever!$)$ of $$1$ per share. Based on this new information, Calculate:

c$.$ The ending cash balance after the dividends are received, selling the stock and paying off your loan.

d$.$ The percentage earned on both the cash purchase and the margin purchase.