Compound Interest Calculation: 8 Months At 1.5%

by SLV Team 48 views

Hey guys! Let's break down how to calculate the future value of an investment with compound interest. This is super useful for understanding how your money can grow over time, so stick with me!

Understanding Compound Interest

Compound interest is basically interest earned on interest. Unlike simple interest, which is only calculated on the principal amount, compound interest calculates interest on the principal plus any accumulated interest. This means your money grows at an accelerating rate. Think of it as a snowball rolling down a hill—it gets bigger and bigger as it picks up more snow! The formula for compound interest is:

A = P (1 + i)^n

Where:

  • A is the future value of the investment/loan, including interest
  • P is the principal investment amount (the initial deposit or loan amount)
  • i is the interest rate per period (as a decimal)
  • n is the number of compounding periods

Let's put this into plain English. Imagine you put some money in a bank account. Each year, the bank pays you interest. With simple interest, you only earn interest on the original amount you deposited. But with compound interest, you earn interest not only on the original amount but also on the interest you earned in previous years. This means your money grows faster over time. For example, if you deposit $100 and earn 10% interest each year, with simple interest, you'd earn $10 each year. But with compound interest, you'd earn $10 the first year, $11 the second year (10% of $110), $12.10 the third year (10% of $121), and so on. As you can see, the amount you earn each year increases over time, leading to faster growth of your investment.

Applying the Formula to the Problem

Okay, now let's use the formula to solve the problem.

  • Principal (P): R$ 8200.00
  • Interest rate (i): 1.5% per month, which is 0.015 as a decimal
  • Number of periods (n): 8 months

Plugging these values into the formula, we get:

A = 8200 (1 + 0.015)^8

Let's break this down step by step:

  1. Calculate (1 + 0.015): 1 + 0.015 = 1.015
  2. Raise 1.015 to the power of 8: 1. 015^8 ≈ 1.1265
  3. Multiply the result by the principal: 8200 * 1.1265 ≈ 9237.30

So, A ≈ R$ 9237.30

Therefore, the amount of the application after 8 months is approximately R$ 9237.30. This is how compound interest works – it helps your money grow exponentially over time. Remember, the longer you leave your money invested, the more significant the impact of compounding becomes. So, start investing early and let the power of compound interest work its magic!

Detailed Calculation Steps

To really understand how we arrived at this answer, let's walk through each calculation step in detail. First, we need to address the interest rate. The problem states that the interest rate is 1.5% per month. To use this in our formula, we need to convert it to a decimal by dividing by 100. So, 1.5% becomes 0.015. This decimal represents the portion of the principal that will be added as interest each month.

Next, we add this decimal to 1 to get the growth factor for each month. This is because each month, the principal is multiplied by this factor to account for the added interest. So, we have 1 + 0.015 = 1.015. This means that each month, the investment grows by a factor of 1.015.

Now, we need to determine the number of compounding periods. In this case, the investment is compounded monthly for 8 months. So, the number of compounding periods is simply 8. This means that the interest is calculated and added to the principal 8 times over the course of the investment.

With all these values in hand, we can now apply the compound interest formula: A = P(1 + i)^n. Plugging in our values, we get A = 8200(1 + 0.015)^8. Let's break this down further. First, we evaluate the expression inside the parentheses: 1 + 0.015 = 1.015. Then, we raise this to the power of 8: (1.015)^8 ≈ 1.1265. Finally, we multiply this result by the principal: 8200 * 1.1265 ≈ 9237.30. This gives us the final amount of the investment after 8 months, which is approximately R$ 9237.30.

Comparing with the Options

Now, let's take a look at the answer options provided:

  • Option A: R$ 9. 237,24
  • Option B: R$ 6. 496,48
  • Option C: R$ 26. 496,48
  • Option D: R$ 9. 184,00
  • Option E: R$ 4. 235,00

Our calculated amount is approximately R$ 9237.30. Comparing this with the options, we see that Option A (R$ 9. 237,24) is the closest to our calculated value. This means that Option A is the correct answer. The slight difference between our calculated value and Option A could be due to rounding differences during the calculation process. However, Option A is still the most accurate choice among the available options.

Why Compound Interest Matters

Compound interest is a powerful tool for wealth creation. The earlier you start investing, the more time your money has to grow. Even small amounts can add up over time thanks to the magic of compounding. It's like planting a tree – the sooner you plant it, the more it will grow. So, don't wait to start investing. Even if you can only afford to invest a small amount each month, it's better than nothing. Over time, those small investments can grow into a significant sum.

Another important thing to keep in mind is the importance of consistent investing. The more consistently you invest, the more your money will grow. Think of it like watering a plant. If you only water it occasionally, it won't grow very much. But if you water it regularly, it will thrive. The same is true for investing. The more regularly you invest, the more your money will grow. So, make it a habit to invest a certain amount each month, and stick to that habit as much as possible.

Finally, it's important to be patient when it comes to investing. Compound interest takes time to work its magic. You won't see huge returns overnight. But if you're patient and stick with it, you'll be amazed at how much your money can grow over time. Think of it like baking a cake. You can't just throw all the ingredients together and expect it to be ready in a few minutes. It takes time for the cake to bake properly. The same is true for investing. It takes time for your investments to mature and grow. So, be patient and don't get discouraged if you don't see results right away. Just keep investing consistently, and eventually, you'll reap the rewards.

Conclusion

So, the final answer is Option A: R$ 9. 237,24. Understanding compound interest is super important for managing your finances and making smart investment decisions. Keep practicing, and you'll become a pro in no time! Investing in learning this stuff really pays off, trust me! Remember to start early, invest consistently, and be patient. With these tips, you'll be well on your way to achieving your financial goals. Happy investing, guys! And remember, the power of compound interest is a powerful tool in building wealth over time, and it can help you achieve your financial goals. So, make sure to take advantage of it and start investing today!