$4$A$).$ We sometimes need to find out how long it will take a sum of money $($or anything else$)$ to grow to some specified amount. For example, if a company's sales are growing at a rate of $20\%$ per year, how long will it take sales to double?

$4$B$).$ If you want an investment to double in $3$ years, what interest rate must it earn?

$4$C$).$ What are the future values of a $3-$year ordinary annuity and annuity due of $$100$ if the appropriate interest rate is $10\%?$

$4$D$)$ What is the effective annual rate $($EAR or EFF$\%)?$ What is the EFF$\%$ for a nominal rate of $12\%,$ compounded semiannually? Compounded quarterly? Compounded monthly? Compounded daily?