What happens if no federal taxes are taken out of my paycheck?

Answers

Answer 1

Maybe your employer simply made a mistake. If your employer has not withheld the correct amount of federal tax, contact your employer to withhold the correct amount for the future.

Who has to pays federal income tax?

Income tax is a tax on the wages and salaries of natural persons, income from capital investments and other income. Payroll taxes, which fund Social Security, Medicare, and unemployment benefits, are the second largest source of federal revenue, accounting for about one-third of total annual revenue.

Who not pay federal taxes?

Generally if your income is below the standard withholding amount, you have a certain number of dependents on your income, you work abroad and are below the required threshold, or you are a qualified non-profit organization If so, you don't have to pay taxes.

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Related Questions

Almost half of all Americans report having less than _________ in savings.
A. $500
B. $1,000
C. $5,000
D. $10,000

Answers

Almost half of all Americans report having less than B. $1,000 in savings.

What are the three main justifications for saving money?

For a variety of reasons, saving is a crucial habit to develop. It helps you cover future costs, manage financial stress, prepare for trips, and more. You could be inspired to save more money if you realise the various ways that saving money can help you prosper.

You have a "negative" net worth if your liabilities exceed your assets. The best moment to start investing is generally not when your net worth is negative. You should reexamine your finances and figure out ways to reduce liabilities, for as by paying down credit card debt.

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a farmer produces peppers in a perfectly competitive market. if the price falls, in the short run the farmer should

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In the short run, the farmer should consider their average variable costs to determine whether they should continue to produce or exit the market.

In a perfectly competitive market, the market price is determined by the interaction of demand and supply, and individual farmers have no control over the price. In such a market, if the price of peppers falls, the farmer must assess their costs to determine the best course of action.

In the short run, the farmer has limited options to adjust their operations. They can reduce their production, but they cannot alter the fixed costs of their operation. If the new lower price is still above the average variable costs, the farmer can continue to produce, but they will need to reduce the quantity they produce to minimize losses.

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true or false: an investment, for example the purchase of shares of stock, should justify not only time the money tied up but also the risk of the investment.

Answers

An investment, for example, the purchase of shares of stock, should justify not only the time the money is tied up but also the risk of the investment. - True

In order to decide whether an investment is worth the risk of a potential loss, the future return on the investment should be compared to the level of risk. The investment's return should be high enough to cover the risk involved. It is up to the investor to decide whether the possible return outweighs the risk because a more significant potential return typically entails a higher level of risk.

It's critical to remember that every investment involves some level of risk and that there is no such thing as a risk-free investment. However, the most important thing is to be aware of the level of risk involved and to make investments in line with risk tolerance and financial objectives.

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Nigel Mccloskey is a waiter at Albicious foods in South Carolina. He is single with one withholding allowance. He receives the standard tipped hourly wage. During the weekending October 22, 20XX, he worked 44 hours and received $170 in tips. Calculate his gross pay, assuming his tips are included in the overtime rate determination. How much does Albicious foods need to contribute to Nigel's wages to meet FLSA requirements? Complete the payroll register for Nigel McCloskey

Answers

The total Gross Pay is  350. To calculate gross pay following formula will be applicable:

Gross Pay = (Hourly wage x 44 hours) + (Hourly wage x 4 hours x 1.5 overtime rate) + Tips

Gross Pay = (7.25 x 44) + (7.25 x 4 x 1.5) + 170

Gross Pay = $350.00

Albicious Foods needs to contribute $350.00 to Nigel's wages to meet FLSA requirements.

Payroll Register for Nigel McCloskey:

Hours Worked: 44  

Hourly Wage: 7.25  

Tips: 170  

Gross Pay: 350

An employee's gross salary is their pay after all tax withholdings have been taken out. A person's net pay is the amount they are paid after all withholdings have been made. Gross pay is calculated as Basic pay plus HRA and other benefits.

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Blossom Co. Began operations on January 2, 2020. It employs 15 people who work 8-hour days. Each employee earns 10 paid vacation days annually. Vacation days may be taken after January 10 of the year following the year in which they are earned. The average hourly wage rate was $20 in 2020 and $21. 50 in 2021. The average vacation days used by each employee in 2021 was 9. Blossom Co. Accrues the cost of compensated absences at rates of pay in effect when earned.


Required:

Prepare journal entries to record the transactions related to paid vacation days during 2020 and 2021

Answers

The journal entries to record the transactions related to paid vacation days during 2017 and 2018 is: Debit Wages expense $28,800; Credit  Vacation wages payable  $28,800.

How to write journal entries?

Journal entries:

1.  2017

Debit Wages expense $28,800

Credit  Vacation wages payable   $28,800

( 15 × 8 hours × 10 days × 24)

2. 2018

Debit Wages expense $1,620                              

Debit  Vacation wages payable $25,920

(15 × 8 hours × 9 days × 24)

Credit Cash   $27,540

(15 × 8 hours × 9 days × 25.50)

3. 2018

Debit Wages expense $30,600

Credit Vacation wages payable      $30,600

( 15 × 8 hours × 10 days × 25.50)

Inconclusion the journal entries to record the transactions related to paid vacation days during 2017 and 2018 is: Debit Wages expense $28,800; Credit  Vacation wages payable  $28,800.

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an accounting professor wants to know the average gpa of the students enrolled in her class. she looks up information on blackboard about the students enrolled in her class and computes the average gpa as 3.29.

Answers

Part a

The statement is ‘True’.            

                             

Part b

The value 3.29 is the population parameter

1. Which of the following statements is true or false? Is the population made up of all accounting class students?

Given statement: The population in the study is all students enrolled in the accounting class.

∵ Therefore, the population in the study is students enrolled in the accounting class.

Part a

The statement is ‘True

All the enrolled students in the accounting class are considered to know the average GPA. Therefore, population is all students enrolled in the class.          

2. Is the 3.29 value the population parameter or the sample statistic?

(b)The value 3.29 represents the population parameter, because it comes from a population of students that are enrolled in the class.

Part ( b)

The value 3.29 is the population parameter.                            

The parameter is the population constant. The value 3.29 is the point estimate the population mean μ . Hence the average GPA is 3.29


INCOMPLETE QUESTION:
an accounting professor wants to know the average gpa of the students enrolled in her class. she looks up information on blackboard about the students enrolled in her class and computes the average gpa as 3.29
1. State whether the following statement is true or false. The population is all students enrolled in the accounting class.

a.) True

b.) False

2. Does the value 3.29 represent the population parameter or the sample statistic?

a.) Population parameter

b.) Sample Statistic


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Businesses that send catalogs and direct mail advertising often buy information about consumers that is collected in an electronic _____________ that tells them what customers buy and from whom they buy merchandise.

Answers

Businesses that distribute catalogues and direct mail advertisements frequently purchase consumer data from an electronic database that informs them of what clients purchase and where they make their purchases.

Accordingly, Exeter will distribute more than 117,000 catalogues. Despite the fact that there are only 50,000 clients in the database, the quantity of goods they have already purchased allows us to send a customer many catalogues and still receive the best results.

Even more expensive and likely to provide subpar outcomes and low sales conversion rates will be mailing every consumer every catalogue or sending them a random selection.

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Sells college textbooks on commission. She gets 10% on the first 7,000 of​ sales, 20% on the next 7,000 of​ sales, and 24% on sales over 14,000 In July of 1997 ​'s sales total was ​$9,500

Answers

College textbooks are commission-based sales at Kelly Price. She receives 8% of the first $7500 in sales, 16% of the subsequent $7500 in sales, and 20% of sales over $20,000 in commission.

How much does commission cost in dollars?

A sales commission is a quantity of money given to an employee when they successfully complete a task, typically selling a specified volume of goods or services. Sales commissions are occasionally used by employers as incentives to raise employee productivity. A commission may be paid instead of or in addition to a wage.

a payment made to a representative or employee in exchange for conducting business on their behalf or providing a service.

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Assume there are no investment projects in the economy that yield an expected rate of return of 25 percent or more. But suppose there are $10 billion of investment projects yielding expected returns of at least 20 percent; another $10 billion yielding at least 15 percent; another $10 billion yielding at least 10 percent; and so forth

Answers

The Aggregate investment of equilibrium will be (a) $20 billion; (b) $30 billion; (c) $40 billion.

This is the investment-demand curve because we have applied the rule of undertaking all investments up to the point where the expected rate of return, r, equals the interest rate,

The total amount of all equity securities owned by Investors, both directly and indirectly, when adjusted for any stock dividends, splits, reverse splits, combinations, recapitalizations, liquidations, reclassifications, mergers, consolidations, or other events

The portion of the year's taxable capital gains that are eligible and exceeds the sum of: the annual permitted capital loss that is eligible. the year's net capital losses from prior years are applied.

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The complete question is given below

Assume there are no investment projects in the economy that yield an expected rate of return of 25 percent or more. But suppose there are $10 billion of investment projects yielding expected returns of between 20 and 25 percent; another $10 billion yielding between 15 and 20 percent; another $10 billion between 10 and 15 percent; and so forth. Cumulate these data and present them graphically, putting the expected rate of return (and the real interest rate) on the vertical axis and the amount of investment on the horizontal axis.

What will be the equilibrium level of aggregate investment if the real interest rate is as follows?

a. 15%: __________ $ billion

b. 10%: ________ $ billion

c. 5%:_________ $ billion

Who is called father of new economics?

Answers

Adam Smith was an eighteenth-century scholar famous as the dad of current financial matters, and a significant defender of free enterprise (non-impedance from the public authority) monetary strategies.

Adam Smith was the 'forefather' of entrepreneur thinking. His supposition that was that people were self-serving commonly yet that as long as each individual were to look for the satisfaction of her/his responsibility, the material necessities of the entire society would be met.

The field started with the perceptions of the earliest financial experts, for example, Adam Smith, the Scottish logician prominently credited with being the dad of financial aspects — even though researchers were mentioning monetary observable facts well before Smith composed The Abundance of Countries in 1776.

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what is the price of star ocean the divine force a long awaited message

Answers

The price of the video game A Long-Awaited Message, Star Ocean: The Divine Force is $59.99

What is the primary objective of gaming?

While it may seem fun, gaming is actually mental exercise. According to studies, playing video games frequently can improve brain connectivity and increase gray matter. Goals, rules, difficulty, and interactivity are crucial game elements. In general, games stimulate the mind or the body, or frequently both.

An electronic stimulant used for fun or education is referred to as a digital game. There are several games that promote physical activity, help people learn useful skills, or have other educational, simulative, or psychological benefits. .Because of its significance to culture, entertainment, and technological growth, the gaming industry is one of the most fascinating sectors of the IT sector.

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Where does the roles of people in the economy come from in a traditional economy?

Answers

In a traditional economy,  the roles of people in the economy come from "the historic success of social customs."

In a society holding a traditional economy, the allocation of resources comes from ritual, habit, or custom. This type of traditional economic system also provides guidance to society since the roles regarding an individual's jobs are defined by the custom of elders and ancestors, that is it is derived from the historic success of social customs.

Traditional economic systems rely on the historic success of social customs.  Asia, Africa, and South America support some traditional economic systems of thriving agricultural villages. Tradition particulars what a person does for their living, so clothing,  industry, and shelter are the same as in previous generations.

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you are trying to decide how much to save for retirement. assume you plan to save $5,000 per year with the first investment made one year from now. you think you can earn 10% per year on your investments and you plan to retire in 43 years, immediately after making your last $5,000 investment. how much will you have in your retirement account on the day you retire?

Answers

We need to find the future value of annuity payments. You can use the pension table to calculate this amount.

$5,000 x 592.4007 (FV of pension, 10%, 43 years) = $2,962,003.50

A U.S. Individual Retirement Account (IRA) is a type of annuity offered by many financial institutions that offers tax incentives for retirement savings.

This is a trust that holds assets acquired with the taxpayer's earned income for the ultimate benefit of the taxpayer's retirement.

An individual retirement account is a type of individual retirement plan described in IRS Publication 590, Individual Retirement Arrangements (IRA).

Other arrangements include employer-sponsored provident funds and individual retirement plans, where taxpayers purchase annuity contracts or endowment policies from life insurance companies.

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What aspect of Lady Bracknells behavior does Wilde use to poke fun at the importance placed?

Answers

He portrays her as unable to discern between a family line and a railroad, between social ties and railroad links, or between a person's ancestry and the location where he happened to be found.

What personality traits would you associate with Lady Bracknell from The Importance of Being Earnest?

First and foremost, Lady Bracknell represents the misery that results from Victorian seriousness. She is strong, conceited, brutal to the point of being severe, traditional, and appropriate. She embodies many of the negative traits, authoritarian attitudes, and authority that Wilde associates with the Victorian upper class.

Instead of being a variant of the name Ernest, the term suggests that one should strive to be earnest, as in being truthful, true, sober, and serious.

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an agent is employed by first patriot bank and trust company of connecticut as a banking representative. the agent is registered in the state with a general securities license through first patriot securities, a separate operating subsidiary of first patriot holdings - the parent company of the bank. a retired couple that is making their monthly visit to the bank to deposit their social security checks asks the agent about the appropriateness of investing in either mutual funds or certificates of deposit. which statement is true regarding the actions that the agent may take when giving a response to these customers?

Answers

The agent can provide general advice about mutual funds and certificates of deposit, but they cannot recommend specific investments, as they are not registered with the state to provide investment advice.

The agent must refer the customers to a financial advisor who is licensed to provide investment advice.

Investing in short-term fixed-income assets is done via money market funds. Government securities such as bonds, Treasury bills, commercial paper, and certificates of deposit are examples of short-term fixed-income assets.

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coordinating day to day activities to achieve the plan

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Daily operations are coordinated to carry out the plan. formulating a strategy to accomplish a company's objectives. Analyzing results against the plan and acting to stay on course

A strategy is a thorough plan to carry out or more broad, lengthy goals in the face of uncertainty. It wasn't until the 18th century that the phrase "art of the general" was translated into Western vernacular languages from Eastern Roman terminology, which dates back to the sixth century C.E. Several subsets of talents, including military tactics, siegecraft, logistics, etc., were included in this concept of the "art of the general." Since then and into the 20th century, the word "strategy" has come to denote "a comprehensive means to try to obtain political ends, including the threat or actual use of force, in a dialectic of wills" in a military fight, in which both adversaries engage. Strategy is essential to achieve goals because resources are frequently limited.

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Name the activities Coordinating day to day activities to achieve.

what was the total amount deducted from lily’s pay for federal, state, and local income tax?

Answers

Lily contributed $14,450 to a retirement 401(k) with her annual gross pay. This amount includes her retirement contribution to a 401(k). The fifth statement is true.

What does a W-2 serve?

Your employer's income, the amount of taxes withheld from your paycheck, the benefits provided, and other information for the year are all shown on a W-2 tax form. You use this form to submit your state and federal taxes.

On my W-2, how do I determine my gross wages?

On most pay stubs, gross wages are typically listed near the top. On a W-2, the total amount your employer paid you, including your salary, hourly wages, tips, commissions, and bonuses, is referred to as your gross wages.

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the main reason that some nations have higher average living standards than others is that a. some nations have stronger laws protecting worker rights. b. the central banks of some nations have created more money. c. the richer nations have exploited the poorer ones. d. some nations have higher levels of productivity.

Answers

The main reason that some nations have higher average living standards than others is that some nations have higher levels of productivity (option d)

Labor productivity is the amount of products and services produced by the average worker in one hour of work. The single most important determinant of a country's quality of living is its level of productivity, with higher productivity growth leading to an ever better standard of living.

Living standards can be evaluated in a variety of ways, but the average annual growth  of the typical household is a reliable indicator for gauging national living standards.

The relationship between productivity and standard of  living is that productivity raises real salaries and income, raising people's standard of life.

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who instigated the scheme in which trading vessels in the indian ocean were required to purchase safe-conduct passes?

Answers

The East India Company instigated the scheme in which trading vessels in the Indian Ocean were required to purchase safe-conduct passes.

The East India Company was a British trading company founded in the early 1600s that had a monopoly on trade between Britain and Asia. They established a network of trading posts and forts across the Indian Ocean, and in order to maintain control over trade in the region, they began requiring all foreign ships passing through the region to purchase "safe-conduct" passes, which were essentially licenses to trade. This scheme allowed the East India Company to extract revenue from foreign traders and maintain a stranglehold on trade in the region, but it was also seen as a form of extortion by other European powers and contributed to tensions in the region.

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which government agency has the ultimate authority to set accounting and reporting standards in the united states?

Answers

The Financial Accounting Standards Board (FASB) government agency has the ultimate authority to set accounting and reporting standards in the united states.

In order to encourage financial reporting that gives investors and other users of financial reports relevant information, the FASB develops and sets financial accounting standards using an open and inclusive process. The FASB is supported and supervised by the Financial Accounting Foundation (FAF).

Companies prepare their accounting information and other economic disclosures in accordance with a set of rules and guidelines known as GAAP. The Board for Financial Accounting Standards (FASB), an independent non-profit organization, creates the standards.

The private sector organization known as the Financial Accounting Standards Bureau (FASB) is in charge of creating the accounting regulations (Accounting Standards) that American businesses adhere to when they publish financial reports. The Generally Accepted Accounting Principles (GAAP) refers to the regulations that the FASB creates (GAAP).

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Is frozen yogurt business profitable?

Answers

Profitability of the frozen yogurt business remains strong substantially because the core product cost is low. Whether you decide to go the  tone- serve route and charge by weight or simply have a flat rate, you will can make a substantial profit.  

Originally targeted at health-conscious  individualities who would tolerate a lumpy, bitter breakfast product, yogurt companies now announce recent changes in  form to meet the  requirements of a wider  followership with a sweet tooth.  

Data Bridge Market Research analyses that the frozen yogurt business request was valued at USD107.2 billion in 2021 and is anticipated to reach the value of USD162.04 billion by 2029, at a CAGR of5.30 during the  cast period.

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those who implement the policies and plans of top management above them and supervise and coordinate the activities of the first-line managers below them are called: multiple choice question. board members. ceos. middle managers. assembly workers.

Answers

Those who implement the policies and plans of top management above them and supervise and coordinate the activities of the first-line managers below them are called: middle managers.

What is the role of Middle managers?

An organization's lower (junior) levels and senior management are connected by a middle manager. Middle managers have the chance to share insightful information and recommendations from within an organization because of their engagement in the day-to-day operations of a corporation. They are in charge of putting into action the rules previously defined in the highest level managers' strategic plans.

Middle managers are in charge of facilitating any organizational changes required and developing a productive workplace. They oversee daily operations, keep track of performance, and ensure that everything is carried out in accordance with the requirements of the business.

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Individuals who are planning a career in selling should understand that
A. the selling process never varies.
B. there is one correct selling process.
C. the selling process is quite simple.
D. there is no single, correct selling process.

Answers

There is no single, correct selling process. Selling is an art and there are many different approaches to successful sales.

What is Selling?

Selling is the process of promoting and exchanging goods and services for money. It involves a seller offering their goods or services to a buyer in exchange for money or other forms of payment. The goal of selling is to attract buyers and convert them into customers. Selling includes a wide range of activities, such as advertising, pricing, product development, distribution, and customer service. It also encompasses market research, communication, and negotiation with potential buyers.

Different selling strategies may be more effective in different situations, and it is important for individuals to understand the different approaches and be able to adjust their strategies to the needs of their customers.

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what pricing model requires the consumer to initially pay to download the app and then offers the ability to buy additional functionality

Answers

Paid apps with in-app purchases requires the consumer to initially pay to download the app and then offers the ability to buy additional functionality.

Users just have to pay once under the premium model in order to download your apps and use all of its features. There aren't any extra fees or in-app purchases. Successful paid applications frequently position themselves as premium experiences through exceptional design, functionality, and marketing since the fee to download may prompt consumers to think more carefully about the app's worth.

Let's examine the most effective methods for doing so as the majority of app developers desire to make money from their apps. The process of creating mobile app pricing models seems straightforward. There are those who devote their life to studying pricing psychology.

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how is your firt week on project excite going? we need to deliver the test version of your product for review in a week

Answers

In this instance, the initiative is deemed to be Highly Useful.

Prior to responding to Nadia, the duties must be prioritized, and a detailed strategy must be created. This would support effective and efficient use of the team members' time. In order to finish the prototype on time, planning also entails dividing up the tasks and duties among the participants.

HIGHLY USEFUL:

To continuously enhance our product and to keep one step ahead of the competition, it is always preferable to be aware of the rivals. We won't be able to assess our product properly without a benchmark against which to compare it.

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COMPLETE QUESTION:

Hi,

How is your first week on Project Excite going? We need to deliver the test version of your product for review in a week. If you need support, let your teammates or me know, and we will do our best to help. Here is everyone’s availability over the next week.

Ravi = fully booked all week

Kara = some time Monday and Friday

Mark = some time Monday and Tuesday

Thanks,

Nadia Loomis

Task

Instructions

With the upcoming deadline, you need help to finish the project. Consider what additional information you would like to know before responding to Nadia.

Question 1 of 4

How useful is knowing the business impact of your project compared to that of your teammates’ other work?

Please rate from Not useful to Highly useful using the buttons below.

Rating 1 of 4, Not useful rating 2 of 4Rating 3 of 4Rating 4 of 4, Highly useful

Not useful

Highly useful

suppose you have worked at a local sandwich shop for six months and now you plan to ask your manager for a raise. how can you convince your manager that you are worth more money than you are currently being paid? a. by threatening to quit if he refuses to give you a raise b. by convincing him that you are a dedicated worker and ready to take on more responsibilities at the shop c. by explaining to him how difficult it is for you to save enough money to go to college d. by showing your manager that your marginal revenue product has increased since your last wage increase

Answers

C. By explaining to him how difficult it is for you to save enough money to go to college. is the correct answer to the given question from the given options.

Option C is the best choice as it demonstrates to your manager your dedication to the shop and your own financial situation.

By explaining to your manager how difficult it is for you to save money for college, you are showing them that you need the extra money in order to progress in life. This will likely help convince your manager that you are worth the raise.

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Carmen Camry operates a consulting firm called Help Today, which began operations on December 1. On December 31, the company’s records show the following selected accounts and amounts for the month of December.
Cash $ 25,330 Dividends $ 5,960
Accounts receivable 22,330 Consulting revenue 26,970
Office supplies 5,210 Rent expense 9,510
Office equipment 19,970 Salaries expense 5,580
Land 43,980 Telephone expense 840
Accounts payable 10,730 Miscellaneous expenses 490
Common stock 101,500 Use the above information to prepare a December income statement for the business.

Answers

Income Statement for the month of December

Revenue: $26,970

Expenses:

Rent expense: $9,510

Salaries expense: $5,580

Telephone expense: $840

Miscellaneous expenses: $490

Total Expenses: $16,420

Net Income: $10,550

Income refers to the money that a company or individual receives as payment for goods or services, or from investments, over a specific period of time, typically a year or a quarter. It is also known as "earnings" or "revenue." In the context of a business, income is the difference between total revenue and total expenses for a given period of time. A positive income means that a company is profitable, while a negative income means that it is operating at a loss.

Here is the calculation for the income statement:

Total Expenses: $9,510 + $5,580 + $840 + $490 = $16,420

Net Income:

Revenue - Expenses = $26,970 - $16,420 = $10,550

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if management is not concerned with the time value of money, from which two capital budgeting methods should they choose? group of answer choices npv or irr. arr or payback. bet or irr. bet or npv. npv or payback.

Answers

According to the question the correct answer is NVP or Payback budgeting method.

What is budgeting method?

Budgeting method is a systematic approach used to plan and manage finances. This method involves setting financial goals, estimating future income and expenses, and determining how to allocate resources in order to meet those goals. Budgeting is a vital component of financial planning and helps individuals, businesses and organizations to keep their finances in check. The most common budgeting methods include zero-based budgeting, incremental budgeting, activity-based budgeting, and line-item budgeting. Zero-based budgeting requires users to start from scratch each time they create a budget, while incremental budgeting is used to adjust existing budgets without having to start from scratch. Activity-based budgeting focuses on resource allocation based on activities, and line-item budgeting is a detailed approach that accounts for each individual expense or income

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no civil liability exists under the uniform securities act if a(n): a issuer offers to sell a security in violation of the act, but no sale occurs b agent omits a material fact when selling a security c terminated agent effects securities transactions for customers before associating with another registered broker-dealer d issuer sells a security without registering the issue in that state, relying on the incorrect advice of counsel that the issue was exempt

Answers

A) an issuer offers to sell a security in violation of the act, but no sale occurs. When a securities company, investor, or broker participates in any activity that gives a false impression about security, including its price, availability, or distribution, market manipulation may take place.

As mentioned above, insider trading takes place when a person exploits information they have about a company's stock for their advantage in a transaction.

When an unqualified person poses as a professional, such as through brokering without a license, it is known as malpractice or ineptitude.

Legal repercussions for violating securities laws could be very harsh. Even a minor infraction can result in criminal misdemeanor charges, which include a fine and/or jail time as penalties. More severe offenses could result in a felony.

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a bank pays 4% nominal annual interest on special three-year certificates. what is the effective annual interest rate if interest is compounded (a) every three months? (b) daily? (c) continuously?

Answers

(a) With compounding every three months, the effective annual interest rate is 4.16%. (b) The effective annual interest rate daily is 4.18%. (c) The effective annual interest rate continuously is 4.19%.

Here's a detailed explanation for each of the three cases:

(a) Compounding every three months:

When interest is compounded every three months, the nominal annual interest rate of 4% is divided by 4 to find the interest rate for each compounding period. To find the effective annual interest rate, we need to find the rate that, if compounded four times per year, would yield the same end result as the nominal rate of 4%. This can be calculated by raising (1 + 0.04/4)⁴ to the power of 1, which is approximately equal to 1.0416.

The formula for compounding interest is A = P * (1 + r/n)^(nt), where A is the end amount, P is the principal, r is the nominal annual interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, we have P = 1 (the starting amount), r = 0.04, n = 4, and t = 1. The interest rate for each compounding period, r/n, is 0.04/4 = 0.01. So the end amount A can be calculated as:

A = 1 * (1 + 0.01)^(4 * 1) = 1 * 1.04^4 = 1 * 1.1658 = 1.1658

The effective annual interest rate, i, is found by dividing the end amount by the starting amount and raising it to the power of 1/t, and subtracting 1:

i = (A/P)^(1/t) - 1 = (1.1658/1)^(1/1) - 1 = 0.0416 or 4.16%

(b) Compounding daily:

When interest is compounded daily, the nominal annual interest rate of 4% is divided by 365 to find the interest rate for each compounding period. The formula for compounding interest is the same as in the first case, with the only difference being that n = 365. This can be calculated using the formula e⁽⁰.⁰⁴⁾ - 1, where e is the mathematical constant approximately equal to 2.718.

In this case, we have P = 1, r = 0.04, n = 365, and t = 1. The interest rate for each compounding period, r/n, is 0.04/365 = 0.00010958904109589. So the end amount A can be calculated as:

A = 1 * (1 + 0.00010958904109589)^(365 * 1) = 1 * 1.04^365 = 1.0418

The effective annual interest rate can be calculated as:

i = (A/P)^(1/t) - 1 = (1.0418/1)^(1/1) - 1 = 0.0418 or 4.18%

(c) Compounding continuously:

When interest is compounded continuously, the nominal annual interest rate of 4% is used to find the continuously compounded interest rate. The formula for continuously compounded interest is A = P * e^(rt), where e is the mathematical constant approximately equal to 2.718. This can be calculated by raising (1 + 0.04/365)³⁶⁵ to the power of 1, which is approximately equal to 1.0418.

In this case, we have P = 1, r = 0.04, and t = 1. So the end amount A can be calculated as:

A = 1 * e^(0.04 * 1) = 1 * 1.0419

The effective annual interest rate can be calculated as:

i = (A/P) - 1 = (1.0419/1) - 1 = 0.0419 or 4.19%

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