Hi everyone! I am Liam, and welcome to the first step in your journey toward financial freedom. Today, we are starting with perhaps the most fundamental concept in the entire world of money: interest. If you want your money to grow, you need to understand how it earns its keep. But here’s the thing—not all interest is created equal. In fact, there is a massive “battle” going on between two different types of growth: simple interest and compound interest. One is like a steady walk up a hill, and the other is like a rocket ship taking off into the stars. We are going to dive deep into both, using the standards from the Ontario curriculum to make sure you can solve these problems on your next test and in your real life. Let’s get started!Hello! I am Maya. I will be your guide through the world of simple interest. Simple interest is exactly what it sounds like: simple. It’s the kind of interest where you only ever earn money on your original investment, which we call the principal. Imagine you put some money into a savings account or a bond. With simple interest, the bank looks at that starting amount—and only that amount—to calculate your reward every year. It is very steady and predictable, which makes it great for short-term planning. But, as we’ll see later, being “steady” might not be enough if you want to build massive wealth over a long period of time. It’s the linear path, and I’m going to show you how to calculate it using tables and logic.Hi there! I am Chloe, and I’m here to show you where the real magic happens. I am representing compound interest. If Maya’s simple interest is a steady walk, my compound interest is a snowball rolling down a mountain. Why? Because with compound interest, you don’t just earn money on your original principal. You earn interest on your interest! This creates a cycle of growth that gets faster and faster the longer you leave it alone. In math terms, this is what we call exponential growth. It’s the difference between adding a few dollars every year and multiplying your wealth. We will see this clearly on our graphs as the compound interest line pulls away from the simple interest line, leaving it far behind in the dust.And I am Noah! I love looking at the big picture and the real numbers. Today, we are going to use some actual math to show you exactly how much money you could be leaving on the table if you don’t understand these two models. We’ll be using tables of values to track the growth year-by-year and graphs to visualize the “Wealth Gap” that forms over time. By the end of this video, you’ll be able to identify which type of growth is happening just by looking at the data. Whether you are in the MCF-3-M or the MBF-3-C course, these skills are vital. Let’s look at our first scenario together.Let’s imagine a scenario where you have one thousand dollars. This is your principal—the starting line for our growth race. You decide to invest this money at a fixed interest rate of ten percent per year. Now, let’s see what happens if you use simple interest. Ten percent of one thousand dollars is exactly one hundred dollars. That means at the end of Year One, you have one thousand one hundred dollars. Simple, right? In Year Two, the bank looks at your original one thousand dollars again. They calculate ten percent of that thousand once more, which is another hundred dollars. Now you have one thousand two hundred. In Year Three, you add another hundred. Every single year, like clockwork, you add exactly one hundred dollars. This is a constant rate of change. On a graph, this forms a perfectly straight blue line. We call this linear growth because the amount of interest you earn never changes. It’s always based on that first thousand you started with.Now, let’s look at my favorite part—compound interest—using that same one thousand dollars and the same ten percent rate. In Year One, things look identical. You earn one hundred dollars and have one thousand one hundred dollars in total. But when we hit Year Two, the “magic” of compounding kicks in. Instead of the bank calculating ten percent of your original thousand, they calculate ten percent of your new total, which is one thousand one hundred dollars! That means you earn one hundred and ten dollars in interest for the second year. Your new total is one thousand two hundred and ten dollars. Did you see that? You just earned an extra ten dollars compared to the simple interest model. That extra ten dollars is “interest on interest.” It’s the money your first-year interest earned for you while you were sleeping!We can see this divergence even more clearly if we look at a table of values over ten or twenty years. In the simple interest column, the interest earned is always one hundred. In the compound interest column, the interest earned grows every single year. One hundred, then one hundred and ten, then one hundred and twenty-one, then one hundred and thirty-three dollars and ten cents. It keeps accelerating. By the time you get to Year Ten, simple interest has left you with two thousand dollars. But compound interest? It has given you two thousand, five hundred and ninety-three dollars and seventy-four cents. That’s nearly six hundred dollars more, just because of how the interest was calculated! This is a major “pro” for your financial life. The longer your money has to compound, the more that interest on interest works for you. This is why financial planners always tell you to start saving as early as possible.When we plot these numbers on a graph, the difference is impossible to ignore. The simple interest line is straight, showing a steady but slow climb. The compound interest line is a curve that gets steeper and steeper as time goes on. This is the definition of an exponential relation. In your math class, you’ll be asked to solve problems using these equations. For simple interest, the total amount $A$ is the principal $P$ plus the interest, which is principal times rate times time: $A = P + Prt$. For compound interest, we use an exponential function: $A = P(1+i)^n$. Don’t worry if those formulas look a bit scary now—we’ll break them down in our next video. For now, the takeaway is this: simple is a straight line, but compound is a powerful curve upward.So, why does this matter for you in Ontario? Well, most savings accounts, G-I-Cs, and long-term investments in Canada use compound interest. This means if you leave your money alone, it will eventually explode in growth. On the flip side, simple interest is more common for very short-term personal loans or some types of consumer credit. Understanding the difference helps you decide where to put your money. If you want to build wealth for the long term, you want compound interest. If you are borrowing money and have the choice, you might prefer simple interest because it doesn’t grow as fast! Seeing the numbers side-by-side on a graph makes it very obvious: compound interest is the clear winner for anyone looking to build wealth over time. In our next lesson, we will dive deeper into the specific formulas and show you exactly how to use your scientific calculator to find your future value. Remember: time is your greatest friend when it comes to compounding. See you in the next video!
