Calculate Simple Interest I = Prt With P = 100 R = 0.13 T = 2

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Understanding Simple Interest

Hey guys! Let's dive into the world of simple interest. Simple interest is a straightforward way to calculate the interest earned on a principal amount. It's a foundational concept in finance and is super useful for understanding loans, investments, and other financial products. The formula we'll be using today is I = prt, which stands for Interest = Principal × Rate × Time. In this formula:

  • I represents the interest earned.
  • p represents the principal, which is the initial amount of money.
  • r represents the interest rate (as a decimal).
  • t represents the time period (usually in years).

Understanding each component of this formula is crucial for accurately calculating simple interest. The principal is the backbone of the investment or loan; it’s the amount upon which interest is calculated. The interest rate determines the percentage of the principal that will be added as interest over a specific period. Time is a critical factor because the longer the money is invested or borrowed, the more interest accrues. It's also super important to express the rate and time in the same units (e.g., if the rate is annual, the time should be in years). Simple interest is often used for short-term loans and investments because it's easy to calculate and understand. However, for longer periods, compound interest, where interest is earned on both the principal and accumulated interest, is generally more beneficial for investments but more costly for loans. Knowing how to work with simple interest is a great starting point for understanding more complex financial calculations, so let’s get started!

Problem Statement: Finding the Interest Earned

So, we have a problem where we need to find the value of I (the interest earned) using the simple interest formula. We're given the following values:

  • p (principal) = $100
  • r (interest rate) = 0.13 (or 13%)
  • t (time) = 2 years

Our mission, should we choose to accept it (and we do!), is to plug these values into the formula and calculate the interest. Before we jump into the calculation, let’s quickly recap what each value represents in our scenario. The principal of $100 is the initial amount we’re working with, think of it as the seed money in our investment. The interest rate of 0.13 (or 13%) is the percentage that will be applied to our principal each year. It’s like the growth rate of our money. The time of 2 years is the duration for which the interest will be calculated. So, our money will be growing at a rate of 13% per year for two years. Understanding these components helps us visualize the problem and make sure our answer makes sense. For example, we know we should expect to earn some interest, and it should be proportional to the principal, rate, and time. If we ended up with a crazy high or low number, we’d know something went wrong in our calculation. With a clear understanding of the problem and the values, we are now fully equipped to calculate the interest earned. Let’s get those numbers crunched!

Step-by-Step Calculation

Alright, let's get down to the nitty-gritty and calculate the value of I. We'll use the formula I = prt. Here’s how we'll break it down step-by-step:

  1. Write down the formula: I = prt

  2. Substitute the given values: We know p = 100, r = 0.13, and t = 2. So, we plug these values into the formula: I = 100 * 0.13 * 2

  3. Perform the multiplication: First, let's multiply 100 by 0.13: 100 * 0.13 = 13 Now, we multiply the result by 2: 13 * 2 = 26

  4. State the result: So, I = 26

Therefore, the interest earned is $26. To recap, we started with the simple interest formula, plugged in the values provided, performed the multiplication in a logical order, and arrived at our final answer. Each step is crucial to ensure accuracy. Missing a step or making a small calculation error can lead to an incorrect result. By breaking it down like this, the calculation becomes much more manageable. It’s like building a house – you lay the foundation first (understanding the formula), then you add the walls (substituting the values), and finally, you put on the roof (performing the calculation). And there you have it, our interest earned is $26! Now, let's discuss what this result means in the context of our problem.

Result and Interpretation

Great job, guys! We've calculated that I = 26. This means the simple interest earned is $26. But what does this really tell us? Let's break it down. The interest of $26 represents the additional money earned on our principal amount of $100 over a period of 2 years, at an interest rate of 13% per year. Think of it as the reward for lending out our money or investing it. After 2 years, our initial investment of $100 has grown by $26, making the total value $126. This is a straightforward example of how simple interest works, and it illustrates the basic principle of earning returns on your money over time. This result is crucial for a few reasons. First, it provides a tangible number that we can use for financial planning. If this were an investment, we'd know exactly how much it grew. If it were a loan, we'd know the exact interest cost. Second, it reinforces the importance of understanding the components of the formula. A higher principal, interest rate, or time period would all result in a higher interest earned. Conversely, a lower value in any of these components would result in less interest. Finally, this calculation serves as a foundation for understanding more complex financial concepts, such as compound interest and the time value of money. Knowing the simple interest allows us to compare it to other investment options or loan structures, helping us make informed financial decisions. So, $26 isn’t just a number; it's a piece of a larger financial puzzle. Now, let's wrap things up with a quick recap and some final thoughts.

Conclusion and Final Thoughts

Okay, let's bring it all together! We successfully found the value of I (simple interest) using the formula I = prt, given p = $100, r = 0.13, and t = 2 years. Our calculation showed that the interest earned is $26. This exercise highlights the importance of understanding and applying the simple interest formula, which is a fundamental concept in finance. By breaking down the problem step-by-step, we made the calculation manageable and easy to follow. Remember, the key to solving these types of problems is to:

  1. Understand the formula: Know what each variable represents and how they relate to each other.
  2. Substitute values correctly: Make sure you plug in the right numbers for each variable.
  3. Perform calculations accurately: Double-check your work to avoid errors.
  4. Interpret the result: Understand what the answer means in the context of the problem.

Simple interest is just the tip of the iceberg when it comes to financial calculations. As you continue your journey in finance, you'll encounter more complex concepts like compound interest, present value, and future value. However, the foundation you've built here with simple interest will serve you well. Keep practicing, stay curious, and never stop learning. Financial literacy is a powerful tool that can help you make informed decisions and achieve your financial goals. So, whether you're calculating interest on a loan, planning for an investment, or just trying to understand how your money grows, the principles we've discussed today will be invaluable. Great job working through this problem with me, and I hope you found it helpful! Keep up the excellent work, and remember, every financial journey starts with a single step—or in this case, a simple calculation!