Disecting Compound Interest

I'm not good at memorizing formulas, so it's easier for me to remember how to calculate compound interest if I break it down and understand it.  Here is the formula:

 So let's break this down:
 A is the amount.  This is the total amount after interest is applied.  This is typically the solution to a simple compound interest problem.
P is the principal.  This is the initial investment amount.
R is the rate of interest.  This rate reflects how many dollars per $100 will be earned.  2.5% means you'll earn $2.50 per $100 invested.
n is the number of times the interest compounds each year.  An annual compound is once, a semi annual compound would be twice, and a quarterly compound would compound 4 times a year.
t is the number of years the interest will be growing the principal.

So what's happening?  For  rate of interest is multiplied by the principal for the first year and then applied to the total amount.  For every next year the total amount will be multiplied by the interest rate, meaning a greater amount of earning occur each year due to the higher total investment.  This is what that looks like:

 

 Earnings grow exponentially because each year (or instance of compound) the earned interest is applied to the total.  The curve of exponential growth is it's steepest after years of compounded interest.  This is why so many retirement commercials are targeting young adults, urging them to start an investment plan early to take advantage of the most steep areas of the growth curve.