The difference between compound and continuously compounded interest is that compound interest changes every year, month, day, etc. while continuous compound interest never stopped changing or growing.
Usually, people choose compound interest over continuously compounded interest for car loan payments, but to determine which would be a better choice, one has to look at the specific situation. The interest rate can make a big difference in the price of a car so it is important to understand it. In addition, the longer you have to pay interest, the higher it will go. Therefore, it is wise to pay off your bills when you are able to as fast as you can. This is just one example of ways interest is used in real life. In fact, this is a very small portion of how math, in general, is used in real life because it is used every day, as previously stated. So, next time you are dreading taking a studying for a test in math, think of that fancy new convertible.
Source: http://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rates/
Spencer Daniels