QUESTION $1$

F$1,$ F$2$ and F$3$ are three financial services companies that charge different interest rates on their loans. F$1$ charges $10\%$ compounded daily, F$2$ charges $10\mathrm{.}1\%$ compounded quarterly, and F$3$ charges $10\mathrm{.}2\%$ compounded semi$-$annually.

a$)$ What is the effective annual interest rate charged by each of the three companies? $($Hint: An accuracy of at least $2$ decimal digits is required$).$

$(10$ Marks$)$

b$)$ Calculate the annual payment a borrower would have to pay to each company on a loan of $$400,000$ over $7-$year period?

$(10$ Marks$)$

c$)$ Which financing company would you prefer?

$(5$ Marks$)$