Why 6% + 6% Doesn’t Equal 12%: The Truth About Compounding Interest

Interest

Ever since I was a child I have found interest to be fascinating. Gaining money passively without any work is quite the concept but calculating the value of interest can be quite confusing to many since it's not simple adding. Compounding interest makes calculating value even more difficult to deduce and measure since differences between interest rates get stretched and exaggerated over time. 

Calculating Interest

So how does calculating interest work anyways? Interest is typically calculated annually, meaning if you had $100 growing at 6% interest you would have $106 at the end of the year. Pretty simple and easy to calculate, but it gets more difficult when you start looking at compounding interest.

Compounding interest is when you make more interest on your interest that you have earned. For example if we look at the above example, you first earn $6 the first year, but the second year it would be 6% of $106 which would equal $112.36 earning an extra 36 cents and the third year $119.10 an extra 74 cents, etc. 

The graph above displays how interest can then earn its own interest which then can then earn more interest into a snowball effect growing at a greater and greater amount each year. You can see that the interest has doubled from $6 at year 1 to $12.07 at year 13.

Linear or Exponential Growth

Now the question of this blog post, does interest add linearly? No it does not. Interest scales exponentially like a rocket flying to mars going faster and faster. Let me explain

Everyone would assume that higher interest would equal higher return which is true and that 10% interest would be double of 5% interest annually which is true but only when looking at a single year. Things get funky when you start looking at compounding interest. The more time elapsed the greater the difference between rates. After 15 years 10% is not simply double 5% but an extra $209.83 greater or about 3x as much. 12% is an extra $307.7 versus 6% over 3x as much. The more time and the greater the interest, the greater the gains or difference you will see. 

On average they say one should be able to double their money every 10 years with investing as a rule of thumb. 

High Interest Rates

It is now easier to understand why rising interest rates can mean huge differences when multiplied by years. Mortgages are normally an individual's largest debt, paid back over 25 years and according to Statsica the average Canadian mortgage is $338,522, which can mean thousands of dollars difference with higher rates. The higher the rate the greater the interest payment will be.

Debt Duration        

Interest payments are the worst or highest in the first years of any debt but especially mortgages since as said before mortgages are large amounts of money paid back over a very long period of time (25 years). Say for example you owe $300,000. At 5% your payment will be $1,744.81 a month.

Your first payment only $507.64 will go to the principal (actual debt) and $1237.17 will be paid to interest which gets you nothing. So in essence you would only be gaining $507.64 of net worth via your house in the first month. But there is good news as it gets slightly better with time. Over the course of 25 years eventually more and more of the monthly payment will go towards the principle and less and less towards interest as the total debt remaining gets lower and lower. 

This means that if there is ever a time to put extra money towards debt it's at the beginning of term as that is when it will make the biggest difference due to the long length of the debt. Some financial coaches recommend always signing up for a 15 year mortgage just to avoid the first 10 years of higher interest that would come in a 25 year mortgage. Of course then there would be the higher interest years in a 25 year but there is always the higher interest period on any length of debt.   

Higher Interest, Higher Debt

So to bring it back. Does 6% + 6% = 12%? No, and this works for debt as well as for investing. 12% payments on a house mortgage is not just twice as bad as 6% it can be 2 or 3 times as bad depending on the term of the mortgage. For example, keeping everything the same in the previous example but using 10% instead, the payments become $2,683.46 or $938.65 more or about 54% higher than the $1,744.81 payments at 5%. Total interest at 10% is $505,038.50 versus $223,444.49 at 5%. It is $281,594.01 more or 126% higher, more than double the amount of interest paid over the 25 years. 

Interest can be confusing but it cuts both ways. It can grow your wealth at an exponential rate and also bleed you of money in debt payments, but with some examples of how interest works and some quick debt or interest calculators you can make better informed decisions about how much debt or investment you take on, for how long and if you want to do extra payments. 

If you found this helpful and would like help budgeting or investing please email me at TaylorMckeeCoaching@gmail.com