Loan Calculation: Farmer's Debt At 11% Interest
Hey guys! Let's dive into this interesting math problem about a farmer clearing his loan. We're going to figure out how much money the farmer initially borrowed from the Co-operative bank. The farmer cleared his dues on a loan taken from a Co-operative bank at 11% per annum (p.a.) after 18 months, paying ₹587.40 as interest. The question we need to answer is: How much money had he taken as a loan? This is a classic simple interest problem, and we'll break it down step-by-step to make sure everyone understands how to solve it. So, grab your thinking caps, and let's get started!
Understanding the Simple Interest Formula
Before we jump into the calculations, it's super important that we all understand the basic formula for simple interest. Simple interest is a straightforward way to calculate the interest on a loan or an investment. Unlike compound interest, which calculates interest on both the principal amount and the accumulated interest, simple interest is calculated only on the principal amount. This makes it easier to compute and understand, which is why it's often used for short-term loans and investments. The formula for simple interest is:
Simple Interest (SI) = (Principal (P) × Rate (R) × Time (T)) / 100
Where:
- Principal (P): This is the initial amount of money borrowed or invested. In our case, it's the amount the farmer initially borrowed, which we are trying to find.
- Rate (R): This is the annual interest rate, expressed as a percentage. In this problem, the interest rate is 11% per annum.
- Time (T): This is the duration for which the money is borrowed or invested, expressed in years. Here, the time is 18 months, which we'll need to convert to years.
Understanding each component of this formula is crucial for solving any simple interest problem. The principal is your starting point, the rate determines how much interest accrues, and the time dictates the period over which the interest is calculated. Make sure you've got these down, guys, because we're going to use them in our calculations!
Converting Time to Years
Alright, so we know that the time period given in the problem is 18 months. But remember, the simple interest formula requires the time to be in years. So, our first step is to convert 18 months into years. This is pretty simple, guys. Since there are 12 months in a year, we can convert months to years by dividing the number of months by 12. So:
Time (in years) = Number of months / 12
In our case:
Time = 18 months / 12 months/year = 1.5 years
So, 18 months is equal to 1.5 years. Now that we've got our time in the correct unit, we're one step closer to solving the problem. It's super important to make sure all your units are consistent before you start plugging numbers into the formula. Otherwise, you might end up with the wrong answer, and we don't want that! Always double-check your units, especially when dealing with time, because it can be given in months, years, or even days. Getting this conversion right is a key part of mastering simple interest problems.
Applying the Simple Interest Formula
Okay, now we're ready to roll up our sleeves and apply the simple interest formula! We know the simple interest (SI), the interest rate (R), and the time (T). What we need to find is the principal (P), which is the initial loan amount. Let's recap what we know:
- Simple Interest (SI) = ₹587.40
- Rate (R) = 11% per annum
- Time (T) = 1.5 years
The formula we're using is:
SI = (P × R × T) / 100
We need to rearrange this formula to solve for P. To do this, we can multiply both sides of the equation by 100 and then divide by (R × T). This gives us:
P = (SI × 100) / (R × T)
Now, let's plug in the values we know:
P = (587.40 × 100) / (11 × 1.5)
This step is where the magic happens, guys! We're taking the formula we discussed and putting in the actual numbers from the problem. Make sure you're following along and understand how we're substituting the values. Once we've plugged in the numbers, the rest is just arithmetic. So, let's move on to the calculation phase and see what the initial loan amount was.
Calculating the Principal Amount
Alright, let's get down to crunching some numbers! We've got the formula all set up, and now it's time to calculate the principal amount (P). Remember, we have:
P = (587.40 × 100) / (11 × 1.5)
First, let's multiply 587.40 by 100:
587.40 × 100 = 58740
Now, let's multiply 11 by 1.5:
11 × 1.5 = 16.5
So, our equation now looks like this:
P = 58740 / 16.5
Now, we just need to divide 58740 by 16.5:
P = 3560
So, the principal amount (P) is ₹3560. This means the farmer initially took a loan of ₹3560 from the Co-operative bank. See, guys? We broke down the problem step by step, and now we have our answer! Calculating the principal amount involves careful arithmetic, so make sure you double-check your calculations to avoid any errors. Accuracy is key in these kinds of problems.
Final Answer and Conclusion
We've done it, guys! After carefully analyzing the problem and applying the simple interest formula, we've arrived at the final answer. The farmer had taken a loan of ₹3560 from the Co-operative bank. This means that the initial amount he borrowed was ₹3560, and over the 18 months, he paid ₹587.40 in interest at an annual rate of 11%.
To recap, here’s what we did:
- Understood the simple interest formula: SI = (P × R × T) / 100
- Converted the time from months to years: 18 months = 1.5 years
- Rearranged the formula to solve for the principal: P = (SI × 100) / (R × T)
- Plugged in the values: P = (587.40 × 100) / (11 × 1.5)
- Calculated the principal: P = ₹3560
This problem is a great example of how we can use simple interest calculations in real-life scenarios. Whether it's figuring out loan amounts, interest payments, or investment returns, understanding these concepts is super valuable. So, next time you encounter a similar problem, you'll be well-equipped to tackle it. Keep practicing, and you'll become a math whiz in no time! Remember, the key is to break down the problem, understand the formulas, and carefully perform the calculations. Great job, everyone!