Problem 73 - Fundamentals of Mathematics

Question

In \(1960,\) the IRS received 1,188,000 corpor ate income tax returns. In 1965,1,490,000 returns were received. In 1970,1,747,000 returns were received. In \(1972-1977,1,890,000 ; 1,981,000 ; 2,043,000 ;\) 2,100,\(000 ; 2,159,000 ;\) and 2,329,000 returns were received, respectively. What was the total number of corpor ate tax returns received by the IRS during the years \(1960,1965,1970,1972-1977 ?\)

Step-by-Step Solution

Answer

Total number of returns: 16,927,000.

Step 1: Identifying the Years with Given Returns

To solve the problem, first identify the years for which the number of corporate tax returns are provided: 1960, 1965, 1970, 1972, 1973, 1974, 1975, 1976, and 1977.

Step 2: Writing Down the Number of Returns

Write down the number of corporate income tax returns corresponding to each year provided: - 1960: 1,188,000 - 1965: 1,490,000 - 1970: 1,747,000 - 1972: 1,890,000 - 1973: 1,981,000 - 1974: 2,043,000 - 1975: 2,100,000 - 1976: 2,159,000 - 1977: 2,329,000.

Step 3: Calculating the Total

Add up the number of corporate tax returns received each year listed to find the total sum:\[\begin{align*}1,188,000 & + 1,490,000 \& + 1,747,000 \& + 1,890,000 \& + 1,981,000 \& + 2,043,000 \& + 2,100,000 \& + 2,159,000 \& + 2,329,000 \\end{align*}\]

Step 4: Performing the Addition

Perform the addition step-by-step: 1. 1,188,000 + 1,490,000 = 2,678,000 2. 2,678,000 + 1,747,000 = 4,425,000 3. 4,425,000 + 1,890,000 = 6,315,000 4. 6,315,000 + 1,981,000 = 8,296,000 5. 8,296,000 + 2,043,000 = 10,339,000 6. 10,339,000 + 2,100,000 = 12,439,000 7. 12,439,000 + 2,159,000 = 14,598,000 8. 14,598,000 + 2,329,000 = 16,927,000

Step 5: Stating the Total Number of Returns

The total number of corporate tax returns received by the IRS during the stated years is 16,927,000.

Key Concepts

IRS data analysis

IRS data analysis is crucial for understanding trends and patterns in corporate tax returns. The Internal Revenue Service (IRS) collects vast amounts of data each year, which can be analyzed to detect changes over time. This type of analysis helps in formulating effective tax policies and making informed decisions.
Analyzing data requires identifying trends and comparing numbers across different years. For example, consider the number of corporate tax returns from 1960 to 1977: we observe an upward trend. Such data enables us to understand how economic conditions and tax laws are impacting corporations over time. It also reveals insights about compliance levels among businesses.
Effective data analysis often involves multiple steps, such as collecting and organizing data. Afterward, careful summation and comparison are needed to draw meaningful conclusions. This makes IRS data analysis an essential tool for researchers, policymakers, and economists.

Addition of large numbers

Adding large numbers can be intimidating at first, but it follows the same basic principles as adding small numbers. The key is to break the problem down and proceed step-by-step.
When adding numbers like 1,188,000 and 1,490,000, align them by their place values and add each column starting from the rightmost digit. Carry over values if necessary. These steps ensure accuracy and prevent errors.
For example:

• First, add the rightmost column (thousands in this instance), including any carryovers.
• Proceed to the next digit to the left, adding each column in turn.
• Continue this process until all digits are added.

Following these steps helps manage and simplify the addition of large numbers. It's often beneficial to add numbers in smaller grouped pairs, as seen in the example, to ensure accuracy and efficiency.

Historical tax data

Historical tax data offers invaluable insights into the economic and fiscal history of a country. By examining corporate tax returns from different years, such as those between 1960 and 1977, trends in economic activities and government policies can be comprehended.
This data helps us understand the rise in returns, which could indicate an increase in the number of businesses or changes in tax regulations during the time. It reflects the economic climate of different decades and helps in assessing how external events impacted tax collection.
By studying historical tax data:

• We can draw comparisons to modern economic environments.
• Identify cyclical trends in economic and tax activities.
• Predict future patterns based on past data.

Understanding historical tax data is essential for economists, policymakers, and history enthusiasts who aim to map the past and envision the future of economic policies.