PROBLEM #$2$: Given a $1\%$ interest rate per month compounded quarterly, calculate $($a$)$ its effective interest rate per month, $($b$)$ its effective interest rate per quarter, $($c$)$ its effective interest per semi$-$annual, and $($d$)$ its effective interest rate per year. Note that for example, effective interest rate per day means effective interest rate per day compounded daily. That is$,$ for an effective interest rate, the payment period must be the same as the compounding period.