Calculating Annual Profit From Simple Interest

Hey guys! Let's dive into a classic math problem that involves simple interest and how to calculate profit. We'll break down the question step-by-step so you can easily understand the concepts. The scenario involves a person who borrows money and then lends it out at a higher interest rate. The goal is to figure out the annual profit they make from this transaction. This kind of problem is super common, so understanding it will definitely come in handy for all you folks out there! In this case, our friend borrows ₹5000 at a 4% annual interest rate for two years. They then turn around and lend the same amount to someone else at a 6.25% annual interest rate, also for two years. The main idea here is that they're earning more interest from the second person than they're paying to the original lender. The difference between these two interests is their profit. So, let's get into the specifics of how to find this profit!

Understanding Simple Interest

Okay, before we get to the calculations, let's quickly recap what simple interest is all about. Simple interest is a straightforward way to calculate the interest on a loan or investment. It's calculated only on the principal amount, which is the original sum of money. The formula for simple interest is pretty simple: Simple Interest = (Principal × Rate × Time) / 100. Where:

• Principal (P) is the initial amount of money.
• Rate (R) is the interest rate per annum (year).
• Time (T) is the time period in years.

So, if you borrow ₹1000 at a 5% simple interest rate for one year, the interest you'll pay is (1000 × 5 × 1) / 100 = ₹50. Super easy, right? This concept forms the foundation of our problem, so keep it in mind as we move forward. Remember that the rate and time must be in the same units (usually per annum, i.e., per year). For example, if the rate is given per month, you have to annualize it by multiplying by 12, the number of months in a year.

This simple interest calculation is fundamental, and you will see it in many financial applications. Understanding simple interest is the first step toward understanding more complex interest calculations, such as compound interest. You can even find online calculators that let you plug in the numbers to determine the simple interest of any transaction. This is a very valuable skill to have, as it allows you to quickly determine how much you're making or losing from an interest transaction.

Calculating the Interest Paid

Alright, let’s start by figuring out how much interest the person pays to borrow the ₹5000. We know the principal (P) is ₹5000, the rate (R) is 4% per annum, and the time (T) is 2 years. Plugging these values into the simple interest formula, we get:

Simple Interest = (5000 × 4 × 2) / 100 Simple Interest = 400

So, the person pays ₹400 in interest over two years. This is the cost of borrowing the money. Now, let’s find out how much interest they earn by lending the same amount to someone else. It's important to keep track of the units of measurement. Remember that the rate is in per annum, and the time is also in years, so we can directly substitute the values into the formula. This ensures that the results are aligned, and there are no issues in the calculations, which is very important in real-world applications where these calculations become more complex.

Remember to double-check the values and units to avoid making mistakes. Simple interest problems like these are often used as an intro to more complex mathematical problems. Keep your eyes sharp and you will be just fine! This simple calculation is a great starting point for understanding financial transactions and is used in a wide range of real-life applications. The basic formula is also applied when calculating the interest paid on loans.

Calculating the Interest Earned

Now, let's calculate the interest the person earns by lending the money at a higher rate. The principal (P) remains ₹5000, but the rate (R) is now 6.25% per annum, and the time (T) is still 2 years. Using the simple interest formula:

Simple Interest = (5000 × 6.25 × 2) / 100 Simple Interest = 625

So, the person earns ₹625 in interest over two years by lending the money. Notice how a small difference in the interest rate can significantly change the outcome. This highlights the importance of finding better rates and understanding how the interest rates work. The interest rate is a key component to understanding how investments and loans operate. Now, we are almost ready to find the profit, which is the goal of our mission.

This step-by-step approach not only helps in finding the solution to the given problem but also enhances the understanding of interest rate and simple interest calculations. Make sure to keep the track of the values during calculation to prevent any errors. Understanding the concept of simple interest is also helpful in many other financial calculations.

Calculating the Annual Profit

Finally, to find the profit, we subtract the interest paid from the interest earned. This gives us the total profit over the two years.

Total Profit = Interest Earned - Interest Paid Total Profit = 625 - 400 Total Profit = 225

So, the person makes a profit of ₹225 over two years. To find the annual profit, we divide the total profit by the number of years:

Annual Profit = Total Profit / Time Annual Profit = 225 / 2 Annual Profit = 112.5

Therefore, the annual profit is ₹112.5. We have now successfully solved the problem by determining the annual profit, which is a great accomplishment! This is how you can calculate the annual profit from this kind of transaction. This kind of calculation is useful for understanding the dynamics of financial transactions. Remember, the annual profit is a useful metric to analyze the efficiency of a loan or investment strategy. The annual profit is a key metric to use when evaluating financial transactions. This problem is straightforward, but it clearly illustrates how one can benefit from the difference in interest rates. Keep practicing, and you'll become a pro at these problems in no time!

To sum it up: By borrowing money at a lower interest rate and lending it at a higher rate, the person earns an annual profit of ₹112.5. We have covered the essentials of simple interest calculations and how to apply them in a real-world scenario. You can always apply this knowledge in everyday situations!

Important Considerations and Tips

Alright, here are some important things to keep in mind when dealing with simple interest problems, and financial transactions in general:

• Always double-check the interest rates. Even a small difference can significantly affect the profit.
• Understand the time period. Ensure the rate and time are in the same units (usually annual). If not, convert them accordingly.
• Be aware of the terms. Know whether you are dealing with simple or compound interest, as the formulas differ greatly. Compound interest includes the interest of the interest, so it might be difficult to calculate manually.
• Use online calculators: They can be incredibly helpful for double-checking your work and for complex scenarios.

This approach not only explains the solution but also helps in enhancing the skills in these calculations. Keep practicing, and you will become skilled at simple interest problems. Remember that the more you practice, the easier it becomes. You will get the hang of these concepts very quickly. Always remember to check your work and keep an eye on the details, as even small errors can impact the outcome. Good luck!

Conclusion

And there you have it, guys! We have successfully calculated the annual profit made by the person. By breaking down the problem into smaller parts and using the simple interest formula, we arrived at the correct answer. The key takeaways here are to understand the concept of simple interest, know how to apply the formula, and always pay attention to the details such as interest rates and time periods. Keep practicing these types of problems to enhance your skills, and you will be a math whiz in no time. This problem is a great example of how simple calculations can lead to valuable financial insights. Good job, everyone!