Suelen's Installment Calculation How To Calculate Simple Interest

Hey guys! Let's break down this math problem step by step so you can totally understand how to calculate Suelen's monthly payments. We've got a scenario where Suelen wants to buy a gadget that costs R$420.00, and she's planning to pay it off in 4 months. But, there's a 3% simple interest charge per month. So, the big question is: How much will Suelen be shelling out each month? Let's dive in and figure it out together!

Understanding Simple Interest: The Key to Suelen's Payments

First off, let's get crystal clear on what simple interest actually means. Simple interest is like the straightforward cousin of compound interest. It's calculated only on the principal amount – the initial cost of the gadget, which is R$420.00 in our case. This means the interest Suelen pays each month is based solely on this original amount and doesn't compound (i.e., the interest isn't added to the principal, and then interest calculated on that new total). This makes it super predictable and relatively easy to calculate. Think of it as the interest no-frills version, perfect for short-term loans and installment plans where things need to be clear and uncomplicated.

Now, why is understanding simple interest crucial here? Well, it's the foundation for determining the total interest Suelen will pay over those 4 months. Once we know the total interest, we can add it to the original cost of the gadget and then divide by the number of months to find the monthly payment amount. So, mastering this concept is the first big step in solving our problem. And don’t worry, we'll take it slow and steady, ensuring everyone's on board before we move on to the calculations!

Calculating the Total Interest: Step-by-Step

Okay, guys, let's get down to the nitty-gritty and calculate the total interest Suelen will be paying. Remember, we're dealing with a simple interest rate of 3% per month. That percentage might seem small, but it adds up over time, so we need to figure out the exact amount. To do this, we're going to use a pretty simple formula: Total Interest = Principal x Interest Rate x Time. This formula is our golden ticket to solving this part of the puzzle.

• Principal: This is the initial amount, the cost of the gadget, which is R$420.00. Think of it as the starting point of our calculation journey.
• Interest Rate: This is the 3% monthly interest, but we need to express it as a decimal for our calculation. So, 3% becomes 0.03. It's all about converting percentages into a usable number format.
• Time: This is the duration of the loan in months, which is 4 months. It's the period over which the interest will be accumulating.

Now, let's plug those numbers into our formula: Total Interest = R$420.00 x 0.03 x 4. Doing the math, we get R$50.40. So, the total interest Suelen will pay over the 4 months is R$50.40. This is a crucial piece of the puzzle – we now know the extra amount Suelen is paying on top of the original cost. Next up, we'll figure out the total amount she needs to pay, including this interest.

Finding the Total Amount to be Paid: Adding Interest to the Principal

Alright, now that we've calculated the total interest, it's time to figure out the total amount Suelen will pay for the gadget. This is a straightforward step: we simply add the total interest to the original price (the principal). Think of it as combining the two parts of the cost – the gadget itself and the extra bit for borrowing the money over time.

We know the principal is R$420.00 (the original cost of the gadget), and the total interest we calculated is R$50.40. So, to find the total amount, we add these together: R$420.00 + R$50.40 = R$470.40. This means Suelen will pay a total of R$470.40 over the 4 months, including the interest. This figure is super important because it's the total pie we need to divide into monthly payments.

Now that we know the total amount, the next step is to divide this by the number of months to find out how much Suelen needs to pay each month. We're getting closer to our final answer, guys! Stay with me as we move on to calculating the monthly installment amount. It's like we're detectives solving a financial mystery, and we're about to crack the case!

Calculating the Monthly Installment: Dividing the Total

Okay, team, we're in the home stretch now! We've figured out the total amount Suelen needs to pay, which is R$470.40. Now, the final piece of the puzzle is to calculate her monthly payment. This is where we divide the total amount by the number of months she's paying for the gadget. It's a simple division, but it gives us the magic number: the amount Suelen will be paying each month.

Suelen is paying over 4 months, so we'll divide the total amount (R$470.40) by 4. Let's do the math: R$470.40 / 4 = R$117.60. This means Suelen's monthly payment will be R$117.60. Voila! We've solved it. It might have seemed complicated at first, but breaking it down step-by-step makes it super manageable.

So, each month, Suelen will pay R$117.60 until the gadget is fully paid off. This includes a portion of the original cost plus the simple interest that has accrued over the month. Now, let's circle back to the original question and see which of the answer options is closest to our calculated amount. This is where we double-check our work and make sure we're selecting the most accurate answer. Let's wrap this up and get Suelen's budget sorted!

Matching the Answer: Finding the Closest Option

Alright, guys, we've done the heavy lifting and calculated that Suelen will pay R$117.60 per month. Now, let's take a look at the options provided and see which one is the closest to our calculated answer. This is a crucial step because sometimes the options might not match perfectly due to rounding or other minor differences. We need to use our judgment to select the best fit.

The options are:

• A) R$ 105,00
• B) R$ 110,00
• C) R$ 115,00
• D) R$ 120,00

Comparing these to our calculated amount of R$117.60, we can see that option D, R$120.00, is the closest. While it's not an exact match, it's the nearest option available. In real-life scenarios, especially in finance, it's super common to see amounts rounded to the nearest whole number or decimal place. This could be why the options don't include the exact amount we calculated.

So, for this question, the best answer is D) R$ 120,00. This is the most reasonable estimate of Suelen's monthly payment based on the options we have. It's always a good idea to choose the closest answer when you don't find an exact match, especially in multiple-choice questions. High five to us for cracking this problem! We've not only found the answer but also understood the process behind it. Let's keep this problem-solving momentum going!

Conclusion: Mastering Simple Interest Calculations

Great job, everyone! We've successfully navigated through the process of calculating Suelen's monthly payments with simple interest. From understanding what simple interest is, to applying the formula, and finally selecting the closest answer, we've covered all the bases. This kind of problem is super common in everyday finance situations, so mastering it is a big win. Whether it's figuring out loan payments, understanding credit card interest, or planning for installments, these skills are invaluable.

Remember, the key to solving these problems is breaking them down into smaller, manageable steps. We started by defining simple interest, then calculated the total interest, added it to the principal, and finally divided by the number of months. Each step built upon the previous one, leading us to the final answer. And don't forget, the formula Total Interest = Principal x Interest Rate x Time is your friend when dealing with simple interest. Keep it in your financial toolkit!

So, what's the takeaway here? With a clear understanding of the concepts and a step-by-step approach, math problems like these become less daunting and even…dare I say…fun! Keep practicing, and you'll become a pro at these calculations in no time. And remember, whether it's for school, work, or personal finance, these skills will serve you well. Now, let's tackle the next financial challenge with confidence!

Final Answer: D) R$ 120,00