Question 703897
Following the hint,
if you calculate the interest earned on $100 both ways:
simple 20% p.a. interest for 2 years,
and 20% p.a. compounded annually for 2 years,
you find that compounded interest gives you $4 more.
To get $48 extra from such compounding, you would need to invest 12 times more, or $1200.

To calculate on year's worth of interest at 20% p.a., we multiply the principal
(the beginning balance) times {{{0.20}}}.
${{{100}}} at 20% interest for 1 year would earn ${{{20}}}.
 
At 20% simple interest for 2 years, the second year interest would be calculated as another ${{{20}}}, based on the starting ${{{100}}}.
The total interest for the 2-year period would be ${{{20}}}+${{{20}}}=${{{40}}}.
 
If the interest was compounded annually,
the balance at the end of the first year,
${{{100}}}+${{{20}}}=${{{120}}},
would be the new principal, used to calculate the interest on the second year.The interest for the second year would be
${{{120(0.20)}}}=${{{24}}}.
That is an extra ${{{4}}} over what simple interest would yield.
The ${{{4}}} for the second year comes from calculating interest on the interest
already earned the first year.
The ${{{4}}} is second year interest on the first year interest.
That's called compounding the interest.
 
NOTE:
Interest can also be compounded monthly, daily, or continuously.