Calculate the future value of

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

in

a$.$

$33$

years at an interest rate of

$6\%6\%$

per year.

b$.$

$66$

years at an interest rate of

$6\%6\%$

per year.

c$.$

$33$

years at an interest rate of

$12\%12\%$

per year.

d$.$ Why is the amount of interest earned in part

$($a$)$

less than half the amount of interest earned in part

$($b$)?$