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Let's test it on the last one we figured out:

If we invest $1.00 in an account that pays 12% compounded  quarterly, how much will we have in the account at the end of one year?

initial amount = $1.00

At the end of each period (quarter), we'll be earning 3%...

So, each $1.00 will turn into $1.03

growth factor = $1.03

number of periods = 4

Here's the formula:

final amount = ( initial amount ) * ( growth factor )^( number of periods )
 

So, with our numbers:

final amount = ( 1.00 ) * ( 1.03 )^( 4 ) = $1.1255088
 

Hey, it works!  We got the same amount that we got doing it the long way...  And this was a LOT easier.