The difference between simple and compound interest is the difference between night and day. You will want to remember this simple rule: simple interest grows slowly, compounding speeds up the process. 

 Simple interest is interest on the principle amount while compound interest is when your principle and any earned interest earned interest. If you have invested money into an account you always want compound interest. Moreover, the relative advantages of compound interest escalate as your holding period increases.

An example might help simplify things.

Suppose you have $100 to invest. You decide to invest it at the Hogg National Bank. It is a small bank located in the heart of Hazzard County. You walk in and speak with the Boss. He says he will pay 10% simple interest on your $100. 

Not knowing he is up to something, you accept the offer and invest your $100. You are all excited and go home and start calculating how much you will have in the future. (Investing is always somewhat exciting!)

Ten percent of $100 is $10 so at the end of 1 year you will have the original principle of $100 + $10 of interest. Still excited you calculate it for the next year. $100 + $10 +10% of the principle which is still 100. So in year 2 you have $120. Mmm…this is not as good as you thought. But you keep going, third year you get another $10. Moreover, if you were to repeat this calculation you would have $10 of interest each year. The reason is that the interest you earn does not get added to the principle amount so you do not earn interest on the interest.

Suppose for the time being that there were another bank in Hazard County (or that you were enlightened enough to invest your money outside of Hazard County) that paid 10% compound interest. That is they paid interest on both your principle as well as the interest you have already earned.

The first year you would be no better off: you would still only have 100(1+interest rate)= 100(1.1)= $110. 

The difference starts in the second year. Now your interest also earns interest. So you would end up with ($100 + $10)(1.1)=$121. This equation can be simplified as

Future value = (present value)* (1+ interest rate) ^{number of years remaining}

The one-dollar difference does not sound like much, this difference gets very large over time. Indeed the difference can get very large if there is enough time. Consider the table below.

You begin off with $100. In each case the money is invested at 10% annual interest. In the two columns your total dollar balance is given.
 

After	Simple Interest	Compound Interest
1 year	110	110
2 years	120	121
3 years	130	133
4 years	140	146
5 years	150	161
10 years	200	259
20 years	300	672
30 years	400	1,744
40 years	500	4,526
50 years	600	11,739

I am sure you agree that it is readily apparent that if you are lending money (and that really is what you do when you give it to the bank to invest), you would prefer compound interest.  Moreover, you would prefer as many compounding periods as possible since at the end of each compounding your account is credited for the interest and thus your interest can start earning more interest.--stop and think about that for a second.   The sooner your interest is credited, the longer it will work for you.  Does it make sense?  Think hard.  It is a key concept. 

As a general rule, we will speak only of compound interest and all of the future and present value tables that are used for calculations assume compound interest. But that is still to come! J
 
 

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