Mosupi is interested in starting a new business and is investigating options for the loan that he would like to secure to get his business off the ground. He consulted his Bank, Madi Bank Limited. Mosupi is interested in obtaining a loan of P$1500000\mathrm{.}00.$ Mosupi is investigating two options based on the offer from his bank, obtaining the loan of P$1500000$ at a simple interest rate of $11\%$ to be repaid over $5$ years or securing a loan at an interest of $11\%$ compounded annually over five years.

Answer the following questions based on the scenario above,

$($a$)$ How much interest would Mosupi have paid at the end of five years if he opted for simple interest rate? $[4$ marks$]$

$($b$)$ How much interest would Mosupi have paid if interest is compounded annually over five years? $[3$ marks$]$

$($c$)$ Based on your answers to $($a$)$ and $($b$)$ what would be your advice to Mosupi in terms of the best option to choose? Support your answer using data. $[4$ marks$]$

$($d$)$ Explain any two factors that determine the amount of interest received by lenders. $[4$ marks$]$