$($Related to Checkpoint$5\mathrm{.}3)($Compound interest with$$ non$-$annual periods$)$Your grandmother just gave you

$$$$10$ comma $00010,000.$

a$.$Calculate the future value of

$$$$10$ comma $00010,000,$

given that it will be invested for

$1010$

years at an annual interest rate of

$33$

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

$66$

percent rather than

$33$

percent$$ rate; recalculate parts

$($a$)$

and

$($b$)$

for an annual interest rate of

$66$

percent.

d$.$Now$$ let's see what might happen if you invest the money for

$2020$

years rather than

$1010$

$$years; recalculate part

$($a$)$

using a time horizon of

$2020$

years$($annual interest rate is still

$33$

$$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?