Compound Interest

One bit of math that everyone must reckon with is compound interest.

You have some money, you earn some interest, that interest gets added to your money, then you earn interest on your money and your previous interest. Good news if you're lending, bad news if you're borrowing. Either way, you should know what you're in for. This is how you calculate it.

P' = P * (1+r/n)^(t * n)
Where
P is the principal, what you start with
P' is how much you end up with after interest has accrued
r is the interest rate, expressed as a decimal, so 4% would be 0.04
t is the amount of time you're considering
and n is where this gets interesting

n is the number of times the interest will be compounded per unit time. So if the interest rate is 4% per year, and you're compounding twice per year, n is 2. If n is assumed to be infinite, the equation turns into

P' = P * e^(r * t)
where e is Euler's Number, 2.718...
I find that form easiest to remember 'cause it spells Pert.

It may seem absurd to take such a thing to infinity, but as you can see above, the result is actually a simpler equation. It also makes sense when you consider that in a real account deposits and withdrawals may be made at any moment. Continuous compounding works on the moment scale.

Einstein may have called compound interest the most powerful force in the universe. But it really is a force of nature. Consider population growth. If the population grows at some rate, the added members of the population will soon be contributing to the growth. This is compound interest. Obviously death, availability of resources and age of maturity temper the effects, but the concept applies.