P$545$ Compounding frequency and time value Fran$$ois plans to invest $$4,000$ in an individual savings account $($ISA$)$ at a nominal interest rate of $6\%.$

a$)$How much will Fran$$ois have in the account after $10$ years if interest is compounded $(1)$ annually, $(2)$ semi$-$annually, and $(3)$ daily $($assuming $365-$day year$).$

b$)$ What is the effective annual rate $($EAR$)$ for each compounding period in part a$?$

c$)$ How much greater will Fran$$ois$$ ISA balance be if the interest is compounded continuously rather than semi$-$annually for the same period?

d$)$ Consider your answers in parts a$,$ b$,$ and c$.$ What does it indicate about the relationship between compounding frequency and the compound value for nominal interest rates?