Investing 101: Compounding

Let's talk about what to do with all that money that you've worked so hard on saving up. In this section titled Investing 101, I'll go over different terms and ideas that every investor should know.* Hopefully the information provided will help give you a general idea of how things work and build a foundation for you to go and further educate yourself. Welcome to class. Today's topic? Compounding.

As Albert Einstein put it, "The most powerful force in the universe is compound interest." Who are we to question the man who gave us the Theory of Relativity and other topics that give physics students fits to this very day? Compound interest is simply interest on interest. Let's take our previous example and build on it.

So we've come to an agreement that I'll return the principal of $100 at the end of the year with an interest rate of 3% giving you a total of $103 in 12 short months. Now let's add a twist. Suppose that I would like to borrow the principal for 2 years instead of one and I give you the option to either take the $3 interest at the end of the first year, or reinvest it so that I am now borrowing $103 for the second year.

If you choose the former, then you will get a total of $6 worth of interest by the end. However, if you chose the latter then you would be receiving $6.09. Where did the extra 9 cents come from? The math would look like this:

Choice 1 and Choice 2

Year 1: $100 x (1.03) = $103

Choice 1                                                                                       Choice 2

Year 2: $100 x (1.03) = $103                                                        Year 2: $103 x (1.03) = $106.09


Add the $3 pocketed in the previous year:  $103 +$3 = $106


For the first year, both options produce the same result; I end up owing you $103. For the second year if the first choice is selected, then you would pocket the $3 and loan me $100 for year two, I end up owing you $103 at the end of the second year and you have a total of $106. If the second choice was selected, then not only do you get 3% of the $100 you lent me, but you also get 3% of the interest that was gained in the previous year (in this case 3% of $3).

Compounding in other words is when the money that you earn through interest is used to earn additional interest. By reinvesting you create a money making machine gives you a larger and larger amount each time that interest is paid. Couple that with the power of time and you can see that everything adds up quickly. 9 cents may not be a lot but over a period of 20 years, if you go with choice 1, then you end up with $160. If you go with choice 2, then you would end up with $180.61 - 12.8% more than the first choice.

Also notice that the more often that interest is paid the larger the difference between the two choices. Calculated over one year (or having the interest being paid once) there is no difference; you end up with the same amount. When interest is paid twice, then the difference is miniscule, with choice two only being 0.06% more than choice one. When interest is paid twenty times then the difference becomes substantial. So the take home message is that monthly interest payments are better than annual ones with all else being equal. Banks usually pay interest monthly for example (so you should really be putting your money in the bank rather than lending it to me).

The magic of compounding works against you when you're on the other side. All the numbers work the same but instead of being on the receiving end, you're paying out the interest. When would you be put into that situation? Mortgages or I don't know... credit card debt [link] comes to mind, especially for the younger adults. With credit card interest being around 20% and calculated monthly, the interest rate is a lot larger and the frequency is a lot more than our example above. That's why it's critical to pay off debt; throw everything at the principal owed before the compounding interest gets out of hand and puts you in the red.

You don't have to be Einstein to see that compounding is be a powerful tool that can help you reach your financial goals. However, having the compounding machine on the other team will put you in a black hole faster than you can say E = mc².

-the Paperboy

*I am by no means an expert and have no background whatsoever on the subjects other than what I learn on my own, so do not take the articles in this series as advice. Please remember to do your own research before making any financial decisions.