Which of the following statements is correct concerning the time value of money?

I. The future value of $$1$ at the end of two years is equal to $$1,00(1+$r$)(1+$r$)$

II$.$ As the interest rate increases for any given year, the future value interest factor will decrease.

III. The future value of $$1$ decreases with the passage of time.

IV$.$ The future value of $$1\mathrm{.}00$ at the end of $2$ years is $$1\mathrm{.}00+2($$$1\mathrm{.}00$ x r$).$

a$.$

I only

b$.$

I and IV only

c$.$

II only

d$.$

II and III only

e$.$

I, II$,$ III and IV