Calculate Simple Interest Earned On $1400 Deposit At 2.5% For 6 Months

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Understanding simple interest is a fundamental concept in personal finance and mathematics. It's the basic way interest is calculated on a loan or investment, and knowing how to compute it can help you make informed decisions about your money. This article will explore the calculation of simple interest earned on a $1400 deposit at an annual interest rate of 2.5% over a period of 6 months. We will break down the formula, apply it to the given scenario, and provide a step-by-step explanation to ensure you understand the process thoroughly. By the end of this article, you'll be able to confidently calculate simple interest for similar scenarios and grasp the underlying principles that govern this financial concept. So, let's dive in and unravel the intricacies of simple interest.

Understanding Simple Interest

Simple interest is a straightforward method of calculating the interest earned on a principal amount. Unlike compound interest, which calculates interest on both the principal and accumulated interest, simple interest is calculated solely on the original principal. This makes it a more predictable and easier-to-understand form of interest calculation. The formula for simple interest is quite simple: Interest = Principal × Rate × Time, or I = PRT. In this formula:

  • I represents the interest earned.
  • P stands for the principal amount, which is the initial sum of money deposited or borrowed.
  • R denotes the annual interest rate, expressed as a decimal (e.g., 2.5% becomes 0.025).
  • T represents the time period, expressed in years. If the time period is given in months, it needs to be converted into years by dividing the number of months by 12. Understanding each component of the formula is crucial for accurate calculations. The principal is the foundation upon which interest is earned, the rate determines the percentage of the principal that will be added as interest, and the time frame dictates how long the principal will earn interest. Now, let's apply this formula to a practical example.

Applying the Simple Interest Formula to the Problem

In this specific scenario, we have a principal amount (P) of $1400 deposited into an account. The account earns an annual simple interest rate (R) of 2.5%, which needs to be converted to a decimal by dividing by 100, resulting in 0.025. The time period (T) is 6 months, which we need to express in years. To do this, we divide 6 months by 12 months per year, giving us 0.5 years. Now that we have all the necessary components, we can plug these values into the simple interest formula: I = PRT. Substituting the values, we get I = $1400 × 0.025 × 0.5. Let's break down the calculation step-by-step. First, we multiply $1400 by 0.025, which gives us $35. This represents the interest earned for one full year. However, since the money is only deposited for 6 months (or 0.5 years), we need to multiply this result by 0.5. So, $35 multiplied by 0.5 equals $17.50. Therefore, the interest earned on the $1400 deposit over 6 months is $17.50. This detailed calculation demonstrates how the simple interest formula works in practice, providing a clear understanding of how each variable contributes to the final interest earned.

Step-by-Step Calculation

Let's break down the calculation into a clear, step-by-step process to ensure complete understanding. This methodical approach will make it easier to follow the logic and apply it to other similar problems. Step 1: Identify the given values. We have the principal amount (P) which is $1400. The annual interest rate (R) is 2.5%, which we convert to a decimal by dividing by 100, resulting in 0.025. The time period (T) is 6 months, which we convert to years by dividing by 12, giving us 0.5 years. Step 2: Write down the simple interest formula: I = PRT. This formula is the foundation of our calculation, and it's essential to have it clearly stated. Step 3: Substitute the values into the formula. We replace P with $1400, R with 0.025, and T with 0.5. This gives us I = $1400 × 0.025 × 0.5. Step 4: Perform the multiplication. First, multiply $1400 by 0.025. This equals $35. So, the equation becomes I = $35 × 0.5. Step 5: Multiply the result by the time period. Multiply $35 by 0.5, which gives us $17.50. Therefore, the interest earned (I) is $17.50. Step 6: State the answer clearly. The interest earned on the $1400 deposit over 6 months is $17.50. By following these steps, you can confidently calculate simple interest for any given scenario. This systematic approach helps to minimize errors and ensures a clear understanding of the calculation process. Now, let's consider the final answer and its implications.

Final Answer and Its Implications

After performing the calculations, we've determined that the interest earned on a $1400 deposit with a 2.5% annual simple interest rate over 6 months is $17.50. This final answer is crucial, but it's equally important to understand its implications. Earning $17.50 in interest over 6 months might seem modest, but it's a return on the initial investment of $1400. In the context of simple interest, this amount reflects the straightforward calculation method where interest is earned only on the principal. This contrasts with compound interest, where interest is earned on both the principal and previously accumulated interest, potentially leading to higher returns over time. The implications of simple interest are significant for both borrowers and lenders. For borrowers, simple interest often translates to lower overall costs compared to compound interest loans, especially for short-term loans. This is because the interest does not accumulate on itself, resulting in a predictable and manageable repayment schedule. For lenders, understanding simple interest helps in accurately projecting returns on investments and loans. It provides a clear picture of the interest income that will be generated over a specific period. Moreover, the concept of simple interest serves as a foundational element for more complex financial calculations and decision-making. It's a stepping stone to understanding concepts like annual percentage yield (APY) and the time value of money. Therefore, grasping simple interest is not just about solving a mathematical problem; it's about building a solid understanding of financial principles that can impact various aspects of personal and professional life. The $17.50 earned in this scenario is a tangible example of how simple interest works, and it underscores the importance of understanding these calculations in the broader context of financial literacy.

Conclusion

In conclusion, we have successfully calculated the simple interest earned on a $1400 deposit at an annual interest rate of 2.5% for a period of 6 months. By applying the simple interest formula I = PRT, we determined that the interest earned is $17.50. This exercise highlights the significance of understanding simple interest calculations in personal finance. Simple interest is a fundamental concept that helps individuals make informed decisions about savings, investments, and loans. It provides a clear and straightforward method for calculating interest, making it easier to predict and manage financial outcomes. The step-by-step approach we used, from identifying the given values to substituting them into the formula and performing the calculations, underscores the importance of a methodical approach to problem-solving in mathematics and finance. Each step plays a crucial role in arriving at the correct answer and ensuring a thorough understanding of the process. Moreover, understanding simple interest serves as a foundation for grasping more complex financial concepts. It's a building block for understanding compound interest, annual percentage yield, and the time value of money, all of which are essential for effective financial planning. Therefore, mastering simple interest calculations is not just an academic exercise; it's a practical skill that can benefit individuals in various aspects of their financial lives. Whether you are saving for a goal, investing for the future, or borrowing money for a significant purchase, a solid understanding of simple interest will empower you to make sound financial decisions and achieve your financial objectives.