Mary said there is no difference between an 8% annual interest rate compounded quaterly and annual interest rate. Explain to mary why she is...

To find the difference  between  (i) 8% annual interest
compounded quarterly and (ii)8 % interest annually.

Let 
Mary invests $10000 with 8% interest
quarterly.

So at at each quarter she gets a quarterly
compound interest of (8/4)% = 2% or 0.02 per dollar.

The
amount A  after the 4 quarters is given by A = Principle * (1+r/4)^4, where r = 8% by
the formula for compound interest with interest.

So at the
end of the year $10000  becomes with interest $10000(1+0.2)^4 =
$10824.32.

I Mary invests the principle P = $10000 in
annual  interest 8%, then the amount A  with interest at the end of the year = A =
P(1+r)^1 = $10000(1+8%)^1 = $10000(1+ 8/100) = $100001.08 =
$10800.

The difference Mary should know is
that she earns a higher amount ($10824.32-10800) = $24.32
if she invests in a quarterly compounding system.