Mary must make payments on $$40,000$ in student loans at $7\%$ interest compounded monthly, a house payment on an outstanding $$100,000$ home loan compounded monthly for $30$ years, and wants to buy a $$35,000$ car. Current interest rates are $5\mathrm{.}5\%$ compounded annually. She owes $$6,000$ on her credit card the charges $1\mathrm{.}5\%$ per month and must make a minimum payment of $50$$ per month on it$.$ She anticipates having $$500$ per month left after meeting expenses, including the minimum payments on loans and her credit card. She is considering investing in the stock market. 

a$)$ What is the minimum MARR she should use to analyze this decision?

b$)$ If she feel she can make $8\%$ each year in the stock market, how should she spend her extra $$500$ per month for the next year?