QUESTION $4$

John, a new graduate who just started his first job, needs to choose between two saving accounts in two different banks. Bank A offers $6\%$ interest per six months, compounded semi$-$annually, while bank B offers $3\%$ interest per three months compounded quarterly.

a$)$ What is the nominal interest rate for each bank?

$(6$ Marks$)$

b$)$ Find the effective annual interest rate for each bank.

$(8$ Marks$)$

c$)$ Which bank would be better for John to save his money in$?$

$(4$ Marks$)$

d$)$ How much should the interest rate $($per $3$ months, compounded quarterly$)$ offered by bank $B$ be so that neither of the two banks is preferred over the other after a year of saving?

Marks$)$