a$)$ You want to invest in a stock that pays $$6\mathrm{.}00$ annual cash dividend for the next $5$ years. At the end of the five years, you will sell the stock for $$30\mathrm{.}00.$ If you want to earn $10\%$ on your investment, what is a fair price to purchase the stock for today?

$(3$ marks$)$

b$)$ Congratulations! You have just won the Caribbean Lottery valued at $25$ million dollars! Under lottery rules, you have been given the option of accepting a onetime lump$-$sum payment of $$5\mathrm{.}2$ million today or equal annual payments for the next $20$ years. What is the annual payment that makes you indifferent to either option?

$(3$ marks$)$

c$)$ You want to buy a house. You have $$20,00,r$ down payment and closing costs. The down payment is $10\%$ and the closing costs are $10\%$ of the loan amount. The bank is willing to allow you to make monthly payments of $30\%$ of your salary at an annual interest rate of $8\%$ for $30$ years, and your annual salary is $$36,000.$ How much can you offer for the house?

$(3$ marks$)$