If you’re reading this, you’re probably planning on going to college, which means your probably going to take out student loans, which probably means you should know a thing or two about how interest works.  You know, interest, as in the extra money you have to pay the bank on the money you borrow, interest as in how much more than you actually spent that you owe your credit card company.

There’s three main kinds of interest: simple, compound and continuously compounded.  Say you decide to put your spring break trip on your credit card… with airfare, hotel, food and whatever else, your tip total is \$3000 (must’ve been a fun week!).  You can’t start paying that off until you get a real job, so you be accumulating interest for (say) three years.  Let’s see how much you’ll actually end up paying for your trip at 12.99% interest using simple annual interest, annually compound interest, and continuously compounded interest.

First we’ll do simple interest:

So with simple interest you’d owe \$4169.10 on the \$3000 you spent on your trip.  Now let’s calculate annually compounded interest.

As you can see, annually compounded interest is a little bit more, you’d owe \$4327.54 on the \$3000 you spent on your trip. Here’s how we figure out continuously compounded interest:

The grand total using continuously compounded interest is \$4429.61.  What does all this math tell us anyway?  Continuously compounded interest is bad! (well, it’s bad if its money you have to pay back, good if it’s in your savings account!). The moral of the story? Interest adds up quick so be careful!