Following the COVID$-19$ pandemic, the banks in South Africa have raised the annual interest rates sharply to $30$ percent $(\%).$ You are a wealthy businessperson and have the option to invest your money either in the bank or to build a small factory for a client.

The total cost of building the factory will be R$12000000,00$ but it will spread evenly over one year $($R$1$ million payable by the end of each month for the next $12$ months$).$ Your client will make a payment of R$3900000,00$ at the end of each quarter from the start of the project.

Your business partner has asked you to provide her with the best scenario to pursue, either to $($a$)$ build the factory for the client, $($b$)$ to invest the money in the bank for a year or alternately to show her that $($c$)$ both options offer the same payoff.

Remember, in order to provide her with the information she requires you will need to discount the cash flows and then determine the return on investment. Remember to show the formula you have used as well as your calculations in full when determining the best option for her. $(15)$