Compounding frequency and time value Personal Finance Problem You plan to invest $$2,100$ in an individual retirement arrangement $($IRA$)$ today at a nominal annual rate of $8\%,$ which is expected to apply to all future years.

a$.$ How much will you have in the account after $9$ years if interest is compounded $(1)$ annually, $(2)$ semiannually, $(3)$ daily $($assume a $365-$day year$),$ and $(4)$ continuously?

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

c$.$ How much greater will your IRA balance be in $9$ years if interest is compounded continuously rather than annually?

d$.$ How does the compounding frequency affect the future value and effective annual rate for a given deposit? Explain in terms of your findings in parts a through $c.$