Your grandmother just gave you $$$$8$ comma $000.$

a$.$Calculate the future value of $$$$8$ comma $000,$ given that it will be invested for $8$ years at an annual interest rate of $5$ percent.

b$.$Recalculate part $($a$)$ using a compounding period that is$(1)$ semiannual and$(2)$ bimonthly.

c$.$Now$$ let's look at what might happen if you can invest the money at a rate of $10$ percent rather than $5$ percent$$ rate; recalculate parts $($a$)$ and $($b$)$ for an annual interest rate of $10$ percent.

d$.$Now$$ let's see what might happen if you invest the money for $16$ years rather than $8$years; recalculate part $($a$)$ using a time horizon of $16$ years$($annual interest rate is still $5$percent$).$

e$.$With respect to the changes in the stated interest rate and length of time the money is invested in parts $($c$)$ and $($d$),$ what conclusions can you$$ draw?