Calcul D'intérêts : Voyage Au Japon

Dec 10, 2025 by Admin 36 views

Hey guys! Let's dive into a cool math problem that's super relevant if you're dreaming of a trip, just like our friend Samy! He's saving up for an awesome adventure to Japan, and he's made a smart move by depositing €1,000 into a savings account on February 24, 2022. This account is earning him a sweet 0.2% monthly interest rate. We're going to break down how his money grows over time. This isn't just about numbers; it's about understanding how your savings can work for you, especially when you've got a big goal like traveling the world!

So, Samy's goal is to fund his future trip to Japan. To get started, he deposited an initial sum of 1,000 euros on February 24, 2022. The bank offers him a monthly interest rate of 0.2%. This means that every month, his initial deposit will earn a little bit more money, thanks to the power of compound interest. We're going to explore two key steps in this financial journey.

First, we need to figure out the total value of Samy's investment after just one month. This will give us a baseline to see how the interest starts working. Then, we'll look at what happens the following month. This second part involves a bit more calculation because the interest earned in the first month will also start earning interest. It's a snowball effect, and it's pretty neat to watch your money grow!

This kind of problem is a classic in mathematics, specifically in the area of financial mathematics or arithmetic and financial progressions. Understanding these concepts can be a game-changer for your personal finance. Whether you're saving for a vacation, a down payment on a house, or just building an emergency fund, knowing how interest works is crucial. It helps you make informed decisions about where to put your money and how long it might take to reach your financial targets. So, let's put on our math hats and crunch these numbers for Samy!

1. Calculating the Value After One Month

Alright, guys, let's tackle the first part of Samy's savings puzzle: figuring out the value acquired by his capital after one month of investment. This is where we see the magic of that 0.2% monthly interest rate kick in for the first time. Remember, Samy started with a principal amount of €1,000. The interest rate is applied monthly, so we just need to calculate one period of interest.

To calculate the interest earned in the first month, we multiply the principal amount by the monthly interest rate. The interest rate is given as 0.2%. To use this in a calculation, we need to convert it into a decimal. So, 0.2% becomes 0.2 / 100, which equals 0.002. Now, let's do the math:

Interest Earned = Principal Amount × Monthly Interest Rate
Interest Earned = €1,000 × 0.002
Interest Earned = €2

See? In just one month, Samy's initial €1,000 has earned an extra €2. Pretty cool, right? But that's not the final value of his investment. The question asks for the value acquired, which means the total amount he has after adding the earned interest to his original principal.

So, to find the total value after one month, we add the interest earned to the initial principal:

Total Value After 1 Month = Principal Amount + Interest Earned
Total Value After 1 Month = €1,000 + €2
Total Value After 1 Month = €1,002

This means that by March 24, 2022, Samy's savings account will show a balance of €1,002. This €1,002 is now his new principal for the next month. This is the fundamental concept of compound interest: interest is earned not only on the initial principal but also on the accumulated interest from previous periods. It might seem small now, but over longer periods, this effect becomes much more significant. So, for Samy's trip to Japan, every little bit of interest counts!

We've successfully calculated the first step. Samy now has €1,002. The next step will involve seeing how this new amount grows further. It's exciting to see how simple calculations can show the power of saving and investing, even with small amounts. Keep this €1,002 in mind as we move on to the next part of the problem, where we'll see how his money continues to grow in the subsequent month. This initial growth, though modest, sets the stage for further accumulation. It's the first step in a longer financial journey, and understanding it is key to appreciating the overall growth potential.

2. The Following Month's Growth

Now, let's get to the exciting part, guys – the growth in the following month! We just calculated that after the first month, Samy's initial €1,000 has grown to €1,002. This new amount, €1,002, is now his principal for the second month. This is where the compound interest really starts to shine. Instead of just earning interest on the original €1,000, Samy will now earn interest on the full €1,002.

The monthly interest rate remains the same at 0.2%, which we've already converted to its decimal form: 0.002. So, let's calculate the interest earned during this second month:

Interest Earned (Month 2) = New Principal × Monthly Interest Rate
Interest Earned (Month 2) = €1,002 × 0.002
Interest Earned (Month 2) = €2.004

So, in the second month, Samy earns €2.004 in interest. You can see it's slightly more than the €2 earned in the first month. This small difference is the direct result of compounding. The extra €0.004 might seem tiny, but over many months and years, this compounding effect can add up significantly. It’s like a snowball rolling down a hill – it picks up more snow and gets bigger and bigger.

To find the total value of Samy's capital at the end of the second month, we add this newly earned interest to the principal from the beginning of the second month (which was €1,002):

Total Value After 2 Months = Principal (Start of Month 2) + Interest Earned (Month 2)
Total Value After 2 Months = €1,002 + €2.004
Total Value After 2 Months = €1,004.004

So, at the end of the second month, Samy's savings will be approximately €1,004.00. Banks typically round to two decimal places for currency, so it would likely be displayed as €1,004.00. This shows a total growth of €4.004 over two months, on an initial investment of €1,000. This is a 4.004% increase in his capital, achieved with a seemingly small monthly rate of 0.2%.

This calculation highlights the power of compound interest. Even with a modest interest rate, consistent saving and allowing interest to compound over time can lead to substantial growth. For Samy's trip to Japan, this means his money is actively working for him, getting him closer to his goal faster than if he just kept the money under his mattress. Understanding this process empowers you to make better financial decisions for your own savings goals, whether it's for travel, education, or any other major life event.

We can generalize this. If 'P' is the principal amount, 'r' is the monthly interest rate (as a decimal), and 'n' is the number of months, the future value 'FV' can be calculated using the formula for compound interest:

FV = P * (1 + r)^n

In Samy's case:

P = €1,000
r = 0.002
n = 1 month (for the first calculation) FV = 1000 * (1 + 0.002)^1 = 1000 * 1.002 = €1,002

And for n = 2 months: FV = 1000 * (1 + 0.002)^2 = 1000 * (1.002)^2 = 1000 * 1.004004 = €1,004.004

This formula confirms our step-by-step calculations and provides a powerful tool for forecasting savings growth over any period. So, keep saving, keep investing, and let that compound interest do its work for you! It’s a fundamental concept in personal finance and a key reason why starting to save early can make such a big difference. For Samy, each month that passes brings him closer to Japan, thanks to his smart financial habits and the bank's interest.

This exercise shows us that consistent saving, even small amounts, coupled with the benefit of compound interest, can significantly boost your financial goals over time. Whether it's for a dream trip like Samy's or other aspirations, understanding these mathematical principles is your first step towards achieving them. Keep these concepts in mind for your own financial planning, guys!