Question

Let \(p\) be a bank's interest rate in percent per year. An initial amount \(A\) has then grown to $$ A\left(1+\frac{p}{100}\right)^{n} $$ after \(n\) years. Make a program for computing how much money 1000 euros have grown to after three years with \(5 \%\) interest rate. Name of program file: interest_rate.py.

Short answer

The money grows to 1157.625 euros after 3 years.

Step-by-step solution

Define Variables

First, identify and define all the variables given in the exercise. We have the initial amount \( A = 1000 \) euros, the interest rate \( p = 5 \% \), and the time period \( n = 3 \) years.

Write the Formula

Next, use the formula provided to calculate the final amount after \( n \) years. The formula is: \[ A\left(1+\frac{p}{100}\right)^{n} \].

Construct the Program

Now, write a Python program named interest_rate.py. Use the formula to compute the result: ```python # Define variables a = 1000 p = 5 n = 3 # Calculate final amount final_amount = a * (1 + p / 100) ** n # Print the result print(final_amount) ```

Execute the Program

Run the Python script to compute the result. The program will print the amount of money, which represents how much 1000 euros grow to in 3 years with a 5% interest rate.

Key concepts

Interest Rate Calculation

Understanding how interest rates affect the growth of your investments is essential in finance. The interest rate is a percentage that signifies how much a sum of money will increase over time. In the context of our exercise, the interest rate is an annual percentage.
To calculate how an initial amount grows over time, we use the formula: \[ A\left(1+\frac{p}{100}\right)^{n} \],where:

• \(A\) is the initial amount of money,
• \(p\) is the annual interest rate, turned into a decimal by dividing by 100,
• \(n\) is the number of years the money is invested or borrowed for.

For our example with an interest rate of 5%, 1000 euros grows according to this exponential formula, reflecting compound interest: interest on the initial amount and interest on interest which accumulates annually.
It's important to realize that compound interest can lead to substantial growth over time, especially with higher interest rates or longer investment periods.

Variables and Formulas in Python

In Python, you can calculate financial formulas by using variables to store data. Variables are symbolic names that stand for values and can be manipulated in mathematical calculations. For this exercise, we represent the initial amount, interest rate, and the number of years as variables.
Here's how we declare and use them in Python:```python# Define variablesA = 1000p = 5n = 3```

• \(A = 1000\) is the initial principal amount.
• \(p = 5\) is the interest rate as a percentage.
• \(n = 3\) indicates the number of years the money is invested.

The next step is to apply the formula using these variables:```python# Calculate final amountfinal_amount = A * (1 + p / 100) ** n```In this calculation, Python follows the order of operations, ensuring the formula is computed correctly. This approach makes Python a powerful tool for performing complex mathematical tasks with minimal code.

Python Script Execution

Running a Python script involves executing a file containing Python code, which performs predefined tasks. In our case, the task is computing how much money our initial 1000 euros will grow to after three years at a 5% interest rate.
Once you've constructed your Python script, named `interest_rate.py`, it's ready to be executed. Here’s a quick guide on how to run your script:

• Ensure you have Python installed on your computer. If not, download it from the official Python website.
• Save your script in a plain text editor such as Notepad or a Python-specific IDE like PyCharm.
• To execute the script, open your command line interface (Terminal on macOS/Linux or Command Prompt on Windows).
• Navigate to the folder containing your `interest_rate.py` file.
• Type `python interest_rate.py` and press Enter to run the file.

Running the script will output the final amount your investment grows to, clearly showing the benefits of using Python scripts for financial calculations. This automation allows for quick adjustments to any of the variables to instantly recalculate results.