Question

The original U.S. income tax of 1913 was quite simple. The tax was \- 1 percent on the first \(\$ 50,000 .\) \- 2 percent on the amount over \(\$ 50,000\) up to \(\$ 75,000\). \- 3 percent on the amount over \(\$ 75,000\) up to \(\$ 100,000\). \- 4 percent on the amount over \(\$ 100,000\) up to \(\$ 250,000\). \- 5 percent on the amount over \(\$ 250,000\) up to \(\$ 500,000 .\) \- 6 percent on the amount over \(\$ 500,000 .\) There was no separate schedule for single or marricd taxpayers. Write a program that computes the income tax according to this schedule.

Short answer

Use a function to calculate tax for progressive income brackets by applying respective rates.

Step-by-step solution

Define the Income Tax Brackets

First, let's list the tax brackets and their corresponding tax rates: - 1% on the first $50,000. - 2% on the amount over $50,000 up to $75,000. - 3% on the amount over $75,000 up to $100,000. - 4% on the amount over $100,000 up to $250,000. - 5% on the amount over $250,000 up to $500,000. - 6% on the amount over $500,000.

Calculate Tax for Each Bracket

To calculate the tax, we will evaluate each bracket sequentially. For each bracket: - Determine the income that fits within the bracket. - Multiply this income by the bracket's tax rate. This step will produce a series of conditional calculations based on the taxpayer's total income.

Implement Income Tax Calculation Function

Write a function that accepts total income as a parameter and computes the total tax based on the defined brackets. For each income threshold: - Check if the income exceeds the threshold. - Apply the tax rate to the appropriate portion of income. - Accumulate the tax from each bracket to derive the total tax.

Code the Income Tax Calculation Logic

```python def calculate_income_tax(income): tax = 0 # Bracket 1: 1% if income > 50000: tax += 50000 * 0.01 else: return income * 0.01 # Bracket 2: 2% if income > 75000: tax += (75000 - 50000) * 0.02 else: return tax + (income - 50000) * 0.02 # Bracket 3: 3% if income > 100000: tax += (100000 - 75000) * 0.03 else: return tax + (income - 75000) * 0.03 # Bracket 4: 4% if income > 250000: tax += (250000 - 100000) * 0.04 else: return tax + (income - 100000) * 0.04 # Bracket 5: 5% if income > 500000: tax += (500000 - 250000) * 0.05 else: return tax + (income - 250000) * 0.05 # Bracket 6: 6% tax += (income - 500000) * 0.06 return tax ``` This code segment computes the tax by iterating over defined income brackets and applying the respective rates.

Key concepts

Python programming

Python is an incredibly versatile language, beloved by many for its readability and efficiency. It is often the language of choice for implementing solutions to problems across a wide range of domains, including finance and data analysis. In the context of computing income tax, Python's straightforward syntax allows us to efficiently construct a program that can process progressively structured conditions, such as tax brackets.

The strengths of Python become evident when dealing with mathematical computations and structured logic. The language facilitates quick prototyping, making it easy for students to experiment with different approaches and solutions. Python's function-based approach enables us to encapsulate the tax calculation logic, creating a reusable function that enhances maintainability and clarity. By accepting parameters, such as the total income, Python functions can process data and return results without altering their behavior for different inputs. This modularity is a key reason why Python continues to be popular among programmers and educators alike.

Tax brackets

Tax brackets are a method of tax calculation where different portions of income are taxed at different rates. This system ensures that taxpayers are taxed fairly according to their earnings, and it becomes particularly relevant in progressive tax systems, such as the original U.S. income tax schedule from 1913.

In this exercise, understanding the concept of tax brackets involves recognizing how income is divided into portions that correspond to specific tax rates. For example, the first \(\)50,000 is taxed at 1%, the income between \(\)50,001 and \(\)75,000 at 2%, and so on. For a taxpayer to correctly compute their total tax, they must apply the appropriate tax rate to each segment of their income based on the bracket thresholds.

Grasping how tax brackets function is crucial, especially when implementing them programmatically. One must ensure that conditions correctly capture these income segments to calculate the tax accurately. This includes setting the right thresholds and applying the correct rates. This concept highlights the importance of logical structuring and precise computation in programming, ensuring every portion of income is adequately taxed as per its respective bracket.

Control structures

Control structures are fundamental in programming, allowing a programmer to dictate the flow of execution based on certain conditions or loops. In tax calculation, control structures, mainly in the form of `if-else` statements, are used to evaluate which tax bracket applies to a given portion of income. These structures help break down a complex problem into manageable conditions.

The provided Python code for tax calculation utilizes a series of `if` statements. They are used to compare the input income against defined thresholds to determine which tax bracket applies. For example, an `if` statement checks if the income is greater than \(\)50,000, and if true, calculates the tax for that bracket. This step-by-step decision-making process continues through the brackets, with each `else` clause capturing the remaining income and executing the corresponding tax calculation.

Understanding how control structures like `if-else` operate is crucial for building logical and functional programs. It helps in automating decisions that would otherwise require manual calculation, thus reducing errors and increasing efficiency. Familiarity with these concepts allows students to construct more complex programs, which are essential skills in any programming career.