QUESTION $1$

Three Canadian banks $x,Y$ and $Z,$ each offers a different effective interest rate on its saving account. The following table provides the nominal interest rate offered by each bank along with the compounding period. $($Hint: Assume $1$ year to be $366$ days$).$

$\backslash$table$[[$Bank$,$Nominal Interest Rate,Compounding Period$],[$X$,8\mathrm{.}25\%,$daily$],[$Y$,8\mathrm{.}25\%,$Monthly$],[$Z$,8\mathrm{.}30\%,$Quarterly$]]$

a$)$ For each of the three banks, find the effective semi$-$annual interest rate.

$(7$ Marks$)$

b$)$ Which bank would you prefer to invest your money in$?$ With that bank, how much interest would you get after $3$ years on a $$5,000$ deposit made now? $($Hint: Use the interest rate calculated in $($a$))$

$(7$ Marks$)$

c$)$ What is the nominal interest rate for a bank that offers $1\mathrm{.}4\%$ interest rate every two months?

$(4$ Marks$)$

d$)$ Considering a new option $($bank $V)$ that offers $9\%$ simple interest rate, would you prefer that bank over the one you chose in $($b$)$ to make an investment now and have the return in $3$ years?

$(7$ Marks$)$