The greatest tool in our toolbox as an investor is compound interest. Understanding compound interest and the impact of time in this equation is of great significance. Compound interest has been called the 8th wonder of the world and phrases like “the magic of compound interest” is used to describe this phenomena. There are several short educational videos on Youtube that try to explain this concept. One of my favorites is from Investopedia. The video is entitled Investopedia Video: Compound Interest Explained and is under 2 minutes in length. I’ll use the same numbers from the video in my scenario to help you understand the key difference between simple interest and compound interest.
Consider this scenario:
Two individuals. Tim and Bob. Both start out with $5,000 to invest. Both have a 5% return on their investment.
Tim starts investing $10,000 for 3 year period and receives 5% simple interest on his principal. Bob, on the other hand, invests the same $10,000 a year for 3 years, but he receives compound interest at 5%. The only difference is the type of interest Tim and Bob receive.
Who will end up with more money at the end of 3 years?
Tim will end up with $11,500 and $1,500 of that will be simple interest. Bob will end up with $11,576.25 and that would include $1,576.25. Bob has $76.25 more because his interest was compounded. The difference of simple interest and compound interest will manifest to a much larger sum over time.
| Tim | Bob | |
| $10,000 | 10,000 | |
| 1yr interest | +$500 | +$500 |
| amount | $10,500 | $10,500 |
| 2yr interest | +$500 | +$525 |
| amount | $11,000 | $11,025 |
| 3yr interest | +$500 | +$551.25 |
| amount | 11,500 | $11,576.25 |
There is a mathematical equation for determining a set amount of money and its compound interest over a length of time. Many people don’t want to take the time to do the math, but it is good to try it yourself because it gives you a better understanding. However, there are several online calculators that may help you determine compound interest as well. Below I’ve included the mathematical equation and what each symbols represents and further down there is a link to an online calculator.
A=P(1+r/n)nt
A= Amount or Future Value
P= Principal
r= interest rate*
* (Remember interest rates are expressed through percentages so 5 percent would be .05)
n= number of times interest is applied per time period (if this is annually this would be 1)
t= number of time periods elapsed (number of years)
I’m going to give you a personal example of the power of compounding interest in one of my Roth IRA Accounts. The IRA acronym stands for Individual Retirement Account and Roth is used to describe this type of account because a former senator from Delaware named William Roth helped establish this type of account in 1997. A Roth IRA is after-tax, meaning you pay taxes on the money before you put it into the Roth IRA, but the returns you earn on your investment will not be taxed when you take it out after you reach retirement age at 59 1/2 or later. In a future blog we will look closer at the two primary IRA’s (traditional IRA and Roth IRA) and the distinct differences of these investment vehicles.
I have a couple Roth Accounts, but the IRS does put conditions on how much an individual can contribute in any given year. Most of my investments, and this one in particular I’m using as an example, are in a type of account known as a balanced mutual fund. Balanced mutual funds is a large basket of stocks and equities along with some bonds. In 2021 it is $6,000 maximum and $7,000 if you’re over the age of 50. In one of my ROTH IRA accounts I had placed $13,805 throughout the years 2003-2012. I have not put any money into this account since 2012 because I have used other vendors and other accounts to continue investing for my retirement. My tax documents from the company or vender I’ve used for this investment only go back 7 years online. So 7 years have passed between 2014 and 2021.
In 2014 I had a total of $34,212.60 in this particular ROTH IRA account.
Let’s see the dates, amounts, and interest rates:
Now let’s look at the math:
A=P(1+r/n)nt
A=$34,212.60(1+.0937/1)1*7
A= $34,212.60(1.871920863729927)
A= $64,043.28
The amount received in returns for 7 years is over $30,000. Astonishing! And, remember, the total amount of my hard earned money I put into this account was $13,805 for a true unrealized gain of $51,321.14. Compounding interest along with time can truly grow wealth.
When I used the online calculator from investor.gov I received this amount $64,043.28 as well. See chart below.
So, somewhere along the line there was a little over a $1,000 variance to my benefit. I came up with $64,043.28 and my account balance from my vendor states I have $65,126.14. However, you can see the math works out exactly to the figures given on the online calculator and also very similarly to the figures in real life. And look at that gap between the green line (amount I had invested) and the red line (amount of my total in that particular account). After learning about compound interest perhaps you understand better how time factors in and why financial experts refer to compound interest as magic. Start saving and create your own magic!
Note: When you try to calculate your future amount of an investment with regular monthly contributions into compounding interest you most certainly will want to use an online calculator instead of trying to do the math manually by long hand.
*Disclaimer: The information provided in this blog and in this website does not and is not intended to constitute financial advice; instead all information, content, and materials presented are for general informational and educational purposes only.
Quest for Fi 