Assume that you are calculating the future value $($FV$)$ of a single sum earning interest at $8\%$ per year, compounded semiannually, for $8$ years.$$ If the compounding were changed to quarterly, then:

A$.$

the number of periods would increase$$ from $8$ to $16.$

B$.$

the rate per period would increase from $2\%$ to $4\%.$

C$.$

the rate per period would decrease from $4\%$ to $2\%.$

D$.$

both A and B$.$

E$.$

both A and C$.$