How to Find the Total Amount Paid in an Interest Rate Equation

How to Find the Total Amount Paid in an Interest Rate Equation.

If you have been given a math problem that requires you to find the total amount of money paid over a certain period of time, don’t worry. These equations are simple to solve if you understand what the parts of the equation are and how to use them.

Method 1 Understanding Interest Rate Equations.
1. Understand the terms you will be working with in your interest rate equation. When you are solving an interest rate equation, such as that for an interest rate you have for a loan you took out, you will work with several different variables. These include.
P = principal amount borrowed.
i = the interest rate.
N = the term of the loan, in years.
F = the total amount paid at the end of the designated number of years.
2. Know the equation used to calculate the total amount you will pay. To find the total amount paid at the end of the number of years you pay back your loan for, you will have to multiply the principal amount borrowed with 1 plus the interest rate. Then, raise that sum to the power of the number of years. The equation looks like this.
F = P(1 + i)^N
3. Read through the equation you are given and determine which numbers coincide with each variable of the equation. Normally, interest rate problems will be given in sentence format and you will have to figure out what each number represents. For example, you are given: “You borrow $4,000 from a bank and promise to repay the loan principal plus the accumulated interest in four years at a rate of 10% per year. How much would you repay at the end of 4 years?”.
P would be $4,000.
i would be 10%.
N would be 4 years.
F would be what you are trying to find.
4. Plug the known numbers into the equation for fixed rate. Once you have figured out what numbers you are working with, you can plug the numbers in so that you can work with the equation to find the fixed rate. Our equation would be:
F = 4000(1 + 10%)^4. Note that to make things easier, you can convert the interest percentage to decimals so the equation would be F = 4000(1 + 0.1)^4

Method 2 Solving an Interest Rate Equation to Find the Total Amount Paid.
1. Work through the problem in stages. In order to find the total amount you will pay over the course of the time you pay back a loan, you will have to work through the article in stages. Let’s look at an example article.
”You borrow 5,000 from a bank and plan to repay the loan principal, plus and accumulated interest in five years. The rate of the interest is 10%. How much will you pay, in total, at the end of the five years?
2. Create your equation. Once you have read through the article, create an equation based on the standard equation F = P(1 + i)^N. For our question, our equation would be:
F = 5000(1 + 0.1)^5.
3. Solve the inside of the parentheses first. When you have written out your equation, start to solve your problem. The first step towards doing this is to solve the equation within the parentheses first. For our equation:
Solve (1 + 0.1) = 1.1. So now our equation looks like this: F = 5000(1.1)^5.
4. Use N to solve the next part of the equation. Once you have simplified the information in the parentheses, you should move onto applying the years (N) of the equation. This means raising the number inside the parentheses to the Nth degree. For our equation:
(1.1)^5 means multiplying 1.1 to itself five times. In this case, (1.1)^5 = 1.61051.
5. Finish the equation. You should now only have one step left in the process of solving your equation. To finish the equation and find F, or the total amount paid, you will have to multiply P with the number in the parentheses. For our equation:
F = 5000(1.61051) therefore, F = $8,052.55. That means that you would have paid $8,052.55 over the course of the five years.

Tips.
Don't forget to chance the interest rate (%) into decimals.

April 10, 2020

How to Calculate an Annual Percentage Growth Rate

How to Calculate an Annual Percentage Growth Rate.

Annual percentage growth rates are useful when considering investment opportunities. Municipalities, schools and other groups also use the annual growth rate of populations to predict needs for buildings, services, etc. As important and useful as these statistics are, it is not difficult to calculate annual percentage growth rates.

Method 1 Calculating Growth Over One Year.
1. Get the starting value. To calculate the growth rate, you're going to need the starting value. The starting value is the population, revenue, or whatever metric you're considering at the beginning of the year.
For example, if a village started the year with a population of 150, then the starting value is 150.
2. Get the final value. To calculate the growth, you'll not only need the starting value, you'll also need the final value. That value is the population, revenue, or whatever metric you're considering at the end of the year.
For example, if a village ended the year with a population of 275, then the final value is 275.
3. Calculate the growth rate over one year. The growth is calculated with the following formula: Growth Percentage Over One Year = {\displaystyle {\frac {FinalValue-StartValue}{StartValue}}*100}{\frac  {FinalValue-StartValue}{StartValue}}*100.
Example Problem. A village grows from 150 people at the start of the year to 275 people at the end of the year. Calculate its growth percentage this year as follows.
Growth Percentage {\displaystyle ={\frac {275-150}{150}}*100}={\frac  {275-150}{150}}*100
{\displaystyle ={\frac {125}{150}}*100}={\frac  {125}{150}}*100
≈ {\displaystyle 0.8333*100}0.8333*100
= {\displaystyle 83.33\%}83.33\%.

Method 2 Calculating Annual Growth over Multiple Years.
1. Get the starting value. To calculate the growth rate, you're going to need the starting value. The starting value is the population, revenue, or whatever metric you're considering at the beginning of the period.
For example, if the revenue of a company is $10,000 at the beginning of the period, then the starting value is 10,000.
2. Get the final value. To calculate the annual growth, you'll not only need the starting value, you'll also need the final value. That value is the population, revenue, or whatever metric you're considering at the end of the period.
For example, if the revenue of a company is $65,000 at the period, then the final value is 65,000.
3. Determine the number of years. Since you're measuring the growth rate for a series of years, you'll need to know the number of years during the period.
For example, if you want to measure the annual revenue growth of a company between 2011 and 2015, then the number of years is 2015 - 2011 or 4.
4. Calculate the annual growth rate. The formula for calculating the annual growth rate is Growth Percentage Over One Year {\displaystyle =(({\frac {f}{s}})^{\frac {1}{y}}-1)*100}=(({\frac  {f}{s}})^{{{\frac  {1}{y}}}}-1)*100 where f is the final value, s is the starting value, and y is the number of years.
Example Problem: A company earned $10,000 in 2011. That same company earned $65,000 four years later in 2015. What's the annual growth rate?
Enter the values above into the growth rate formula to find the answer:
Annual Growth Rate {\displaystyle =(({\frac {65000}{10000}})^{\frac {1}{4}}-1)*100}=(({\frac  {65000}{10000}})^{{{\frac  {1}{4}}}}-1)*100
{\displaystyle =(6.5^{\frac {1}{4}}-1)*100}=(6.5^{{{\frac  {1}{4}}}}-1)*100
≈ {\displaystyle (1.5967-1)*100}(1.5967-1)*100
= 59.67% annual growth.
Note — raising a value a to the {\displaystyle {\frac {1}{b}}}{\frac  {1}{b}} exponent is equivalent to taking the bth root of a. You will likely need a calculator with an "{\displaystyle n{\sqrt {x}}}n{\sqrt  {x}}" button, or a good online calculator.

FAQ.

Question : Say that my company projects the next three years' revenue, 2016 with $300,000, 2017 with $350,000, and 2018 with $320,000. What is the percentage increase or decrease in revenue?
Answer :  2017 compared to 2016 an increase of 17%; 2018 compared to 2017 a decrease of 8.6%
Question : If my house value doubled in 12 years, what was the percentage rate growth each year?
Answer : The compound annual rate of growth is 6%. Calculate that by using the "Rule of 72": Divide 72 by the number of years it takes an investment to double in value, and that is the compound rate of growth over the period of time applied.
Question : I started with 125 members in a group. 3 years later, we now have 700 members in the group, what is our growth percentage in 3 years?
Answer :  Your growth rate has been 460% over 3 years.
Question : How can I calculate the percentage of population change in the decade?
Answer :  Take the population at end of the decade. Subtract it from population at beginning of decade. That is the total population change. Convert to a percentage. Divide the population change by the population at beginning of the decade. Multiply by 100.
Question : What is the annual increase of 3% of 2600?
Answer : 3% of 2600 is (.03)(2,600) = 78.
Question : What does the upside "v" mean?
Answer : To the power of. It's a common way to write out powers when a number can't be formatted as a superscript. 2^2 means 2 squared, for example.
Question : How did it go from (6.5^1/4-1) * 100 to (1.5967 -1) * 100? You didn't explain how you got rid of the "1/4" or how you ended up with 1.5967? Can you please clarify?
Answer :  (6.5^1/4-1)*100 would be represented as (6.5^0.25-1)*100. This is how you get to (1.5967-1)*100.
Question : The population of my town is 100,000. How many years will it take for the population to double at an average annual growth of 0.5 %?
Answer : Using the formula for "doubling time" (t = 70 / r, where t is time in years, and r is the annual rate of growth), the doubling time in this case is 70 / 0.5 = 140 years.

April 09, 2020

What percentage of political science majors are female

FAQ What percentage of political science majors are female

By many measures, women in political science do not achieve the same success as men. Their ranks among full professors are lower; their teaching evaluations by students are more critical; they hold less prestigious committee appointments; and, according to a new study, their work is cited less frequently.

Why? And what can be done to change this? Those questions absorbed two panels here at the American Political Science Association's annual meeting on Thursday. The problems are not new, and most likely not limited to political science. But the researchers who presented their findings hope that hard data and some serious self-reflection will spark change within the discipline.

"We are not the first people to talk about bias in academe, but the trick has been to show evidence that in fact this exists," said Barbara F. Walter, a political-science professor at the University of California at San Diego and co-author of a new paper showing a gender citation gap in international relations.

In that paper, "The Gender Citation Gap," Ms. Walter and her colleagues found that even after controlling for many variables—including what the subjects wrote about, the methodology they used, and where they worked—women were cited less frequently than men were. In their review of more than 3,000 journal articles published from 1980 to 2006, articles by men received an average of 4.8 more citations than were articles by women. (The average number of citations per article over all was 25.)

The authors came up with two explanations: Women tend to cite their own work less than men do, which can have a multiplying effect as time goes by. And men, who dominate the profession, tend to cite other men more than they cite women.

The state of gender politics in political science is not nearly as “far from ideal” as it once was (Judith Shklar, quoted in Hoffman 1989, 833) but neither is it gender-neutral. The “inhospitable institutional climate” cited in the 2005 American Political Science Association (APSA) Report on the Status of Women in Political Science persists in multiple subtle (and sometimes not-so-subtle) ways, as well as in certain spaces (i.e., departments, conferences, and subfields) far more than in others.

One of the most obvious areas of gender disproportionality is in the methodology subfield. When areas of the field lag behind in gender integration, it is cause for concern. This is particularly acute for political methodology, however, because it is both a gender-integration laggard and the area of the field that develops the “rules of the game” for good political science. As such, political methodology is not simply a standalone subfield in the discipline; it also informs the work done in most other subfields. The lack of diversity in political methodology, therefore, raises the uncomfortable possibility that some of our “rules of the game” may embed biases based on the relative privilege of those making them.

Given the disproportionate focus on and status of highly complex statistical methodology within political science as a whole, the fact that such methodology is far more likely to be the province of men than women is concerning, from both a methodological standpoint and a gendered perspective. As practitioners and critical observers of this discipline, and as methodology instructors ourselves, we are concerned about the increasing status of complex statistical methodology (and the perception that it is somehow “better” than qualitative or far simpler quantitative work) as well as persisting gender disparities in the field—and we see these trends as linked. To be clear, our aim is not to rehash the qualitative-versus-quantitative debate but rather to add a new angle: this cleavage in research methods is not gender-neutral.

Anecdotes like Tamara’s abound but systematic data on these questions can be difficult to find or collect. Therefore, this article presents a theory based on initial data rather than well-tested hypotheses, but these are ideas worthy of discussion and further testing. What systematic data we have found—coupled with useful previous literature and our own experiences—allow us to posit a complex and interactive set of gender-related forces operating within political science and particularly affecting graduate students.

Specifically, we suggest that there are two contextual themes and four overlapping processes that operate individually and jointly to reinforce—and reproduce—the overrepresentation of men in subfields that emphasize complex quantitative methodology (including formal theory). The two contextual factors are the discipline’s long history of male domination and the more recent hegemony of quantitative methodology within political methodology and political science overall. Within this context, we find evidence suggesting four interconnected but distinct processes that continue to advantage men within the discipline overall but particularly in areas privileging complex quantitative methodology: (1) initial departmental admission-selection biases by gender; (2) subfield-selection biases by gender; (3) gendered attrition in response to experiences in the field; and (4) gender bias in disappointment when methodology dominates substantive content.

This article examines and explains each element (contextual and procedural) in turn, using the evidence we can find. Overall, we call this a theory of gendered selection and survival biases. Initial selection biases favoring graduate-student applicants with highly quantitative backgrounds are more likely to result in men than in women in graduate cohorts. This is especially true in the study of political methodology because of the gender breakdown in college studies in math, hard science, and statistics. Furthermore, methodological practices that confuse the ends (substance) with the means (methods), we suggest, are more of a turnoff within the field for women as a group than for men as a group—although they also turn off many men who care deeply about the political substance of political science.

Within this context, we find evidence suggesting four interconnected but distinct processes that continue to advantage men within the discipline overall but particularly in areas privileging complex quantitative methodology: (1) initial departmental admission-selection biases by gender; (2) subfield-selection biases by gender; (3) gendered attrition in response to experiences in the field; and (4) gender bias in disappointment when methodology dominates substantive content.

The result is a concentration of women in some subfields (especially comparative politics) and the dominance of political methodology by men, which has adverse effects on the discipline. A more inclusive science, which embraces multiple methods as well as types of people, will be stronger for the wider set of perspectives and questions brought to bear on major political problems. Using multiple methods within a single project also makes it stronger by allowing for triangulation of results arrived at through different pathways, giving greater confidence in a study’s findings. Diversity of thought, perspectives, concerns, questions, and approaches makes for better as well as more-inclusive science.

In the conclusion, we provide suggestions for best practices that departments can engage in (based on both real-world examples and theory) to move toward this better, more inclusive science. Many departments and professors work extremely hard to combat the gender imbalances we describe, often with success, and we want to disseminate their examples while urging others to do the same.

Find More What percentage of political science majors are female

May 25, 2019

How did Warren Buffett get started in business?

How did Warren Buffett get started in business?

By BRENT RADCLIFFE.
Warren Buffett may have been born with business in his blood. He purchased his first stock when he was 11 years old and worked in his family’s grocery store in Omaha.
His father, Howard Buffett, owned a small brokerage, and Warren would spend his days watching what investors were doing and listening to what they said. As a teenager, he took odd jobs, from washing cars to delivering newspapers, using his savings to purchase several pinball machines that he placed in local businesses.

His entrepreneurial successes as a youth did not immediately translate into a desire to attend college. His father pressed him to continue his education, with Buffett reluctantly agreeing to attend the University of Pennsylvania. He then transferred to the University of Nebraska, where he graduated with a degree in business in three years.

After being rejected by the Harvard Business School, he enrolled in graduate studies at Columbia Business School. While there, he studied under Benjamin Graham – who became a lifelong friend – and David Dodd, both well-known securities analysts. It was through Graham's class in securities analysis that Buffett learned the fundamentals of value investing. He once stated in an interview that Graham's book, The Intelligent Investor, had changed his life and set him on the path of professional analysis to the investment markets. Along with Security Analysis, co-written by Graham and Dodd it provided him the proper intellectual framework and a road map for investing.

Benjamin Graham and The Intelligent Investor.
Graham is often called the "Dean of Wall Street" and the father of value investing, as one of the most important early proponents of financial security analysis. He championed the idea that the investor should look at the market as though it were an actual entity and potential business partner – Graham called this entity "Mr. Market" – that sometimes asks for too much or too little money to be bought out.

It would be difficult to summarize all of Graham's theories in full. At its core, value investing is about identifying stocks that have been undervalued by the majority of stock market participants. He believed that stock prices were frequently wrong due to irrational and excessive price fluctuations (both upside and downside). Intelligent investors, said Graham, need to be firm in their principles and not follow the crowd.
Graham wrote The Intelligent Investor in 1949 as a guide for the common investor. The book championed the idea of buying low-risk securities in a highly diversified, mathematical way. Graham favored fundamental analysis, capitalizing on the difference between a stock's purchase price and its intrinsic value.

Entering the Investment Field.
Before working for Benjamin Graham, Warren had been an investment salesman – a job that he liked doing, except when the stocks he suggested dropped in value and lost money for his clients. To minimize the potential of having irate clients, Warren started a partnership with his close friends and family. The partnership had unique restrictions attached to it. Warren himself would invest only $100 and, through re-invested management fees, would grow his stake in the partnership. Warren would take half of the partnership’s gains over 4% and would repay the partnership a quarter of any loss incurred. Furthermore, money could only be added or withdrawn from the partnership on December 31st, and partners would have no input about the investments in the partnership.

By 1959, Warren had opened a total of seven partnerships and had a 9.5% stake in more than a million dollars of partnership assets. Three years later by the time he was 30, Warren was a millionaire and merged all of his partnerships into a single entity.
It was at this point that Buffett’s sights turned to directly investing in businesses. He made a $1 million investment in a windmill manufacturing company, and the next year in a bottling company. Buffett used the value-investing techniques he learned in school, as well as his knack for understanding the general business environment, to find bargains on the stock market.

Buying Berkshire Hathaway.
In 1962, Warren saw an opportunity to invest in a New England textile company called Berkshire Hathaway and bought some of its stock. Warren began to aggressively buy shares after a dispute with its management convinced him that the company needed a change in leadership..  Ironically, the purchase of Berkshire Hathaway is one of Warren’s major regrets.
Understanding the beauty of owning insurance companies – clients pay premiums today to possibly receive payments decades later – Warren used Berkshire Hathaway as a holding company to buy National Indemnity Company (the first of many insurance companies he would buy) and used its substantial cash flow to finance further acquisitions.

As a value investor, Warren is a sort of jack-of-all-trades when it comes to industry knowledge. Berkshire Hathaway is a great example. Buffett saw a company that was cheap and bought it, regardless of the fact that he wasn’t an expert in textile manufacturing. Gradually, Buffett shifted Berkshire’s focus away from its traditional endeavors, instead using it as a holding company to invest in other businesses. Over the decades, Warren has bought, held and sold companies in a variety of different industries.

Some of Berkshire Hathaway’s most well-known subsidiaries include, but are not limited to, GEICO (yes, that little Gecko belongs to Warren Buffett), Dairy Queen, NetJets, Benjamin Moore & Co., and Fruit of the Loom.  Again, these are only a handful of companies of which Berkshire Hathaway has a majority share.
The company also has interests in many other companies, including American Express Co. (AXP), Costco Wholesale Corp. (COST), DirectTV (DTV), General Electric Co. (GE), General Motors Co. (GM), Coca-Cola Co. (KO), International Business Machines Corp. (IBM), Wal-Mart Stores Inc. (WMT), Proctor & Gamble Co. (PG) and Wells Fargo & Co. (WFC).

Berkshire Woes and Rewards.
Business for Buffett hasn’t always been rosy, though. In 1975, Buffett and his business partner, Charlie Munger, were investigated by the Securities and Exchange Commission (SEC) for fraud. The two maintained that they had done nothing wrong and that the purchase of Wesco Financial Corporation only looked suspicious because of their complex system of businesses.
Further trouble came with a large investment in Salomon Inc. In 1991, news broke of a trader breaking Treasury bidding rules on multiple occasions, and only through intense negotiations with the Treasury did Buffett manage to stave off a ban on buying Treasury notes and subsequent bankruptcy for the firm.
In more recent years, Buffett has acted as a financier and facilitator of major transactions. During the Great Recession, Warren invested and lent money to companies that were facing financial disaster. Roughly 10 years later, the effects of these transactions are surfacing and they’re enormous.

A loan to Mars Inc. resulted in a $680 million profit.
Wells Fargo & Co. (WFC), of which Berkshire Hathaway bought almost 120 million shares during the Great Recession, is up more than 7 times from its 2009.
American Express Co. (AXP) is up about five times since Warren’s investment in 200813
Bank of America Corp. (BAC) pays $300 million a year and Berkshire Hathaway has the option to buy additional shares at around $7 each – less than half of what it trades at today.
Goldman Sachs Group Inc. (GS) paid out $500 million in dividends a year and a $500 million redemption bonus when they repurchased the shares.

Most recently, Warren has partnered up with 3G Capital to merge J.H. Heinz Company and Kraft Foods to create the Kraft Heinz Food Company (KHC). The new company is the third largest food and beverage company in North America and fifth largest in the world, and boasts annual revenues of $28 billion. In 2017, he bought up a significant stake in Pilot Travel Centers, the owners of the Pilot Flying J chain of truck stops. He will become a majority owner over a six-year period.
Modesty and quiet living meant that it took Forbes some time to notice Warren and add him to the list of richest Americans, but when they finally did in 1985, he was already a billionaire. Early investors in Berkshire Hathaway could have bought in as low as $275 a share and by 2014 the stock price had reached $200,000, and was trading just under $300,000 earlier this year.

Comparing Buffett to Graham.
Buffett has referred to himself as "85% Graham." Like his mentor, he has focused on company fundamentals and a "stay the course" approach – an approach that enabled both men to build huge personal nest eggs. Seeking a seeks a strong return on investment (ROI), Buffett typically looks for stocks that are valued accurately and offer robust returns for investors.
However, Buffett invests using a more qualitative and concentrated approach than Graham did. Graham preferred to find undervalued, average companies and diversify his holdings among them; Buffett favors quality businesses that already have reasonable valuations (though their stock should still be worth something more) and the ability for large growth.

Other differences lie in how to set intrinsic value, when to take a chance and how deeply to dive into a company that has potential. Graham relied on quantitative methods to a far greater extent than Buffett, who spends his time actually visiting companies, talking with management and understanding the corporate's particular business model. As a result, Graham was more able to and more comfortable investing in lots of smaller companies than Buffett. Consider a baseball analogy: Graham was concerned about swinging at good pitches and getting on base; Buffett prefers to wait for pitches that allow him to score a home run. Many have credited Buffett with having a natural gift for timing that cannot be replicated, whereas Graham's method is friendlier to the average investor.

Buffett Fun Facts.
Buffett only began making large-scale charitable donations at age 75.
Buffett has made some interesting observations about income taxes. Specifically, he's questioned why his effective capital gains tax rate of around 20% is a lower income tax rate than that of his secretary – or for that matter, than that paid by most middle-class hourly or salaried workers. As one of the two or three richest men in the world, having long ago established a mass of wealth that virtually no amount of future taxation can seriously dent, Mr. Buffett offers his opinion from a state of relative financial security that is pretty much without parallel. Even if, for example, every future dollar Warren Buffett earns is taxed at the rate of 99%, it is doubtful that it would affect his standard of living.

Buffett has described The Intelligent Investor as the best book on investing that he has ever read, with Security Analysis a close second. Other favorite reading matter includes:
Common Stocks and Uncommon Profits by Philip A. Fisher, which advises potential investors to not only examine a company's financial statements but to evaluate its management. Fisher focuses on investing in innovative companies, and Buffett has long held him in high regard.
The Outsiders by William N. Thorndike profiles eight CEOs and their blueprints for success. Among the profiled is Thomas Murphy, friend to Warren Buffett and director for Berkshire Hathaway. Buffett has praised Murphy, calling him "overall the best business manager I've ever met."
Stress Test by former Secretary of the Treasury, Timothy F. Geithner, chronicles the financial crisis of 2008-9 from a gritty, first-person perspective. Buffett has called it a must-read for managers, a textbook for how to stay level under unimaginable pressure.
Business Adventures: Twelve Classic Tales from the World of Wall Street by John Brooks is a collection of articles published in The New Yorker in the 1960s. Each tackles famous failures in the business world, depicting them as cautionary tales. Buffett lent his copy of it to Bill Gates, who reportedly has yet to return it.

The Bottom Line.
Warren Buffett’s investments haven't always been successful, but they were well-thought-out and followed value principles. By keeping an eye out for new opportunities and sticking to a consistent strategy, Buffett and the textile company he acquired long ago are considered by many to be one of the most successful investing stories of all time. But you don't have to be a genius "to invest successfully over a lifetime," the man himself claims. "What's needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework."

August 04, 2020