Savology - Compound Interest - How it works

You don’t necessarily have to wake up at 4:00 AM every morning, do 50 push-ups a day, or read a book a week to become a millionaire.

While some surveys have correlated similar behaviors to success, amassing a nest egg of $1,000,000 or more is much more straightforward than you might assume.

Let’s use the example of cigarettes and coffee…

According to a recent Fair Reports article, the lowest cost for a pack of cigarettes can be found in Virginia and Missouri at $5.25. The highest cost is in New York at $12.85. The report shows the average cost in the US is $7.04.

Based on my conversations with smokers, most smokers report they smoke about a pack a day. If you don’t smoke, maybe you drink coffee? Two cups of coffee from a coffee shop would have a very similar cost.

So if someone were to quit smoking or drinking overpriced coffee and save that money instead, how long would it take to be a millionaire? 

At $7.04 per day, that works out to around $2,569.60 every year. At that annual rate, it would take saving that amount under your mattress for 389.17 years to save a million dollars. That’s a long time, isn’t it? 

But wait a minute… You aren’t just going to sleep on the money. Instead, you could be earning interest!

Earning interest on your money

Here is a quick example to demonstrate the basics of earning interest.

With simple interest, each year you would earn interest on the amount you saved or contributed.  So $100 of principal contributed at a 10% annual interest rate will earn $10.00 interest in one year, bringing the total to $110.00. In the second year, you would earn another $10.00, bringing the total to $120.00. 

Using simple interest, it would decrease the amount of time that it would take to be a millionaire down to 79 years. If you were earning 10% on $2,569.60 contributed each year, you would make $256.96 per year for each $2,569.60 contribution. 

If we multiply this out, in year 79, we would have $200,428.80 in total contributions, $20,042.88 in total interest for year 79, and $771,650.88 as the sum of interest for the previous 78 years (Σ$256.96 x number of contributions for each year).  This comes out to about a million dollars.

As you can see here, earning interest on your principal is great. But there is an even better way. The better way is an investment phenomenon known as compound interest.

What is compound interest and how does it differ from simple interest?

Compound interest differs from simple interest in two primary regards.

First, compound interest pays interest on the principal and the interest, not just the principal. Effectively, this means that the interest you receive is added to the principal for the next interest calculation.

Second, interest can be compounded on any frequency schedule. This means that the interest can be added back into the equation every year, every month, every day, or continuously. 

The good news is that most accounts are continually compounding. In other words, the accounts compound infinitely many times per year, each time adding a small fraction of a cent. 

If we continuously compounded $1 for a year at 10% interest it would grow to $1.105170918 by the end of the year. That may not seem like much, but these small increments add up, and then they compound and add up again.

Applying this to the $100 principal example, if you were to have continuously compounded interest instead of simple interest at the same 10%, the $100 would become $110.52. This is certainly better than $110.00. But the bigger difference comes in year 2 and beyond. Instead of $120.00 after the second year, you would have $122.14.

If we took into account interest earned on interest, and then the interest earned on that interest, and that interest and so forth, how long do you think the pack a day habit would make us a millionaire?  

This is where the stock market comes in. The average return of the S&P 500 since its inception in 1926 has been about 10% annually.  This varies greatly from year to year but would be appropriate to use in modeling the growth of investments in the market. Even though the stock market doesn’t pay out traditional interest, the concept of equity returns applies similarly. And with stock market returns, compounding is inherent.

Based on this 10% annual return of the S&P 500, with an investment of $2,569.60 per year, it would theoretically take less than 39 years to reach $1,000,000.

But how?!

You would make 38 annual contributions of $2.569.60 totaling $97,644.80. The rest (over $900,000) would come from interest or returns throughout the 39 years! Do you know how long the average working career is? It is 40 years for most, and even longer for some!

While how much you save is important, the real secret to savings is time. The formula to calculate compound interest is an exponential function. Exponential functions have a growth curve that increase its rate of increase over time. They all begin accelerating their rate of acceleration given enough time.  But that is the problem: time! The earlier you save, the less you have to save to reach that million dollars.   

Start compounding your interest today

At the end of the day, it isn’t really about smoking cigarettes or drinking expensive coffee, it is about saving money consistently and compounding the effects of that. Albert Einstein called compound interest the “8th wonder of the world” and can you blame him? Now that you know exactly how compound interest works, you can put the principle to work for you by starting to save early and often while investing for retirement.


Your financial future starts today

Savology is a free financial planning platform providing fast and free financial planning. In just five minutes you can get access to a free, unbiased, personalized financial plan. Your Savology plan will give you tailored action items to start working on as well as an overview of your financial progress so that you can continue making improvements. As you complete action items and modules, you’ll receive new ones to stay motivated and working towards your financial goals.

Recommended Posts