Simple Interest Calculation: Complete The Table

Oct 16, 2025 by Dimemap Team 48 views

Hey guys! Let's dive into a simple interest problem. We've got Eduardo, who's made a smart move by investing some capital. To understand the financial growth, we’ll walk through the concepts of simple interest and how to calculate it, then apply these calculations to complete a table. This will not only solve the problem but also give a solid grasp of how simple interest works. Let's get started!

Understanding Simple Interest

In the world of finance, simple interest is a straightforward way to calculate the interest earned on an investment or loan. Unlike compound interest, which calculates interest on both the principal amount and the accumulated interest, simple interest is calculated only on the principal. This makes it easier to understand and predict the returns or costs associated with the investment or loan. To really grasp simple interest, let's break down the key components and the formula we'll use.

The core components of simple interest are the principal amount, the interest rate, and the time period. The principal amount (P) is the initial sum of money invested or borrowed. In our case, Eduardo invested R$2,500.00, which is our principal. The interest rate (r) is the percentage charged or earned on the principal over a specific period, usually expressed as an annual rate, but it can also be monthly, quarterly, or any other period. Here, the interest rate is 2% per month. Time (t) is the duration for which the money is invested or borrowed, typically measured in years or months, depending on the interest rate's period. For this problem, we’re looking at a time frame of 1 to 4 months.

The formula for calculating simple interest (SI) is quite simple:

SI = P * r * t

Where:

SI is the simple interest earned.
P is the principal amount.
r is the interest rate (as a decimal).
t is the time period.

To use this formula effectively, it’s crucial to express the interest rate and time period in consistent units. If the interest rate is given per month, the time period should be in months. If the interest rate is annual, the time period should be in years. Now that we understand the formula and its components, let's move on to applying it to Eduardo's investment. This will make the concept even clearer and show you how simple it is to calculate the interest earned over different periods. Remember, understanding simple interest is fundamental in many financial calculations, from personal investments to loans, so paying attention here will really pay off in the long run!

Calculating Interest for Eduardo's Investment

Alright, now that we've got the theory down, let's get practical and calculate the interest Eduardo will earn on his investment. Remember, Eduardo invested R$2,500.00 at a simple interest rate of 2% per month. We’re going to use the simple interest formula, SI = P * r * t, to figure out the interest earned for 1, 2, 3, and 4 months.

First, let's identify our variables:

Principal (P) = R$2,500.00
Interest rate (r) = 2% per month, which is 0.02 when expressed as a decimal
Time (t) = 1, 2, 3, and 4 months

Now, we'll calculate the interest for each time period:

For 1 month (t = 1):
```
SI = 2500 * 0.02 * 1
SI = R$50.00
```
So, after 1 month, Eduardo earns R$50.00 in interest.
For 2 months (t = 2):
```
SI = 2500 * 0.02 * 2
SI = R$100.00
```
After 2 months, the interest earned is R$100.00.
For 3 months (t = 3):
```
SI = 2500 * 0.02 * 3
SI = R$150.00
```
Eduardo earns R$150.00 in interest after 3 months.
For 4 months (t = 4):
```
SI = 2500 * 0.02 * 4
SI = R$200.00
```
After 4 months, the interest earned is R$200.00.

Now that we've calculated the interest for each period, we can see how the interest grows linearly with time in simple interest scenarios. This step-by-step calculation illustrates the simplicity of simple interest and how it directly relates to the principal, interest rate, and time. Next, we'll organize these results into a table, making it easy to visualize the interest earned over the specified periods. This will give us a clear picture of Eduardo’s investment growth over time.

Completing the Table

Okay, we’ve crunched the numbers and now it's time to organize our results into a table. This will give us a clear and concise view of the interest Eduardo earns over the 1 to 4-month period. Tables are super helpful for visualizing data, and in this case, it will make it easy to see the relationship between time and interest earned. Let's build the table step by step.

We’ll create a table with two columns: Time (in months) and Interest (in R$). The time column will list the months (1, 2, 3, 4), and the interest column will show the corresponding interest earned for each month, which we calculated in the previous section. Here’s how the table will look:

Time (Months)	Interest (R$)
1	50.00
2	100.00
3	150.00
4	200.00

As you can see, the table neatly summarizes the interest earned for each month. After 1 month, Eduardo earns R$50.00, after 2 months he earns R$100.00, and so on. The interest increases by R$50.00 each month, which is a direct result of the simple interest calculation. The consistent increase makes it easy to predict the interest earned for future months as well.

This table not only provides a clear picture of the interest earned but also highlights the linear nature of simple interest. Each month, the interest earned is the same because it’s calculated only on the principal amount. This is different from compound interest, where the interest earned also earns interest, leading to exponential growth. Now that we’ve completed the table, we have a solid understanding of Eduardo’s investment growth over time. This exercise demonstrates how organizing financial information in a table can make it easier to understand and analyze. In the next section, we’ll recap the entire process and highlight the key takeaways from this problem.

Conclusion: Key Takeaways from Eduardo's Investment

Alright, guys, we've reached the end of our journey through Eduardo's simple interest investment! We started with the initial problem, broke down the concept of simple interest, calculated the interest earned over different periods, and then organized our findings into a clear and concise table. Let's take a moment to recap the key takeaways from this exercise. Understanding these points will not only help you solve similar problems but also give you a solid foundation in financial calculations.

First, we revisited the definition of simple interest, which is the interest calculated only on the principal amount. Unlike compound interest, simple interest doesn't take into account the accumulated interest from previous periods. This makes it straightforward to calculate and predict. We used the formula SI = P * r * t, where SI is the simple interest, P is the principal, r is the interest rate, and t is the time. This formula is the cornerstone of simple interest calculations, and mastering it is crucial.

Next, we applied this formula to Eduardo's investment, where he invested R$2,500.00 at a simple interest rate of 2% per month. We calculated the interest earned for 1, 2, 3, and 4 months. The step-by-step calculations showed us how the interest grows linearly over time. For example, after 1 month, Eduardo earned R$50.00, and after 4 months, he earned R$200.00. This consistent growth pattern is a hallmark of simple interest.

Then, we organized these results into a table, which provided a clear visual representation of the interest earned over time. The table highlighted the direct relationship between the time period and the interest earned, making it easy to analyze the investment’s performance. Tables are incredibly useful tools for organizing and presenting financial data, and this example demonstrates their effectiveness.

In summary, understanding simple interest is fundamental in financial literacy. It provides a basis for understanding more complex interest calculations and investment strategies. By working through Eduardo’s investment, we’ve not only solved a problem but also reinforced the key principles of simple interest. Keep practicing these calculations, and you'll become more confident in your ability to handle financial scenarios. Whether it's calculating interest on a loan or predicting the returns on an investment, a solid understanding of simple interest is a valuable asset. Great job, everyone, for sticking with it, and I hope you found this explanation helpful and engaging! Until next time!