CourseIntroduction to financial mathematics, notions of percentage, calculations of simple and compound interest, simple and compound discounts, equivalence of capital at interest, fixed incomes, and loan amortization.For the student- HAZZAN, Samuel; POMPEO, José Nicolau. Financial Mathematics. Saraiva, 2007.For the teacher- GIMENES, Cristiano Marchi. Financial mathematics with Hp 12c and Excel. 2006.- CÉSAR, Benjamin. Financial Mathematics: theory and 700 questions. Ed. Campus, Rio de Janeiro–RJ, 5th Edition, 2005.- CARVALHO, Sérgio; CAMPOS, Weber. Simplified Financial Mathematics for Exams. 2010.IntroductionFinancial Mathematics aims to study the value of MONEY over TIME. Taking as a scenario money investments and loan payments.Do you remember how much each item cost 30 years ago?Money changes its value over time, which makes it extremely difficult to compare amounts from decades ago with current amounts. Generally, value declines, due to numerous factors. We call this decline inflation. Inflation is not necessarily bad; it is a natural phenomenon that occurs in the economy. If your salary rises above or equal to inflation, there is no panic.Inflation is even healthy when compared with deflation. A deflationary scenario means that everyone's wages are rising even while they remain still. To keep the balance, salaries tend to be cut. Salary cuts make workers unhappy, which generates dissatisfaction and stoppages. In addition, deflationary scenarios mean that the consumer is consuming little or that, in the long term, it can generate an economic problem.Despite this, very large inflations are also not welcome. Hyperinflation scenarios bring uncertainty and make it difficult for businesspeople to think about economic scenarios. Zimbabwe recently went through hyperinflation:We call CAPITAL any monetary amount that a person (individual or legal entity) lends to another for a certain time. From one perspective, it can also be designated as the initial amount.Given that the lender refrains from using the lent amount and, furthermore, because of the loss of purchasing power of money due to inflation and the risk of default, the concept of INTEREST arises.INTEREST can be defined as the cost of the loan (for the borrower) or the compensation for the use of capital (for the lender).We call the interest rate the amount of interest in a certain unit of time, expressed as a PERCENTAGE of the capital.Finally, at the end of a financial transaction, the sum of the capital and the interest is called the AMOUNT, which is the final value found.Percentage"Per cent" is the same as "divided by 100." And its '%' symbol is precisely reminiscent of a mixed-in 100.Every number except irrational numbers can be expressed as a percentage. The use of percentages is due to the ease of visualizing values by having only to divide them by 100 (an easy process for human beings who use the decimal numbering system). Which of the following is easier to see?\[{1\over2} \text{ is double } {1\over4}\]\[50\% \text{ is double } 25\%\]Percentage expresses a proportion or a relationship between 2 (two) values, thus maintaining proportionality for comparison, unlike the use of the nominal value of money. Instead of always adjusting the interest amount according to the capital, percentage is used because it is constant in different systems and thus allows them to be compared. Invest 1000 reais and earn 100, or invest 500 reais and earn 60? In the first case the interest is 10%, and in the second 12%. The use of percentage in this case makes it clear which would be the better investment!The best way to calculate the percentage of a number is using the rule of three:\[2\%\text{ of }300\]\[{2\over100}={x\over300}\]\[{x={2\over300*100}=6}\]ExercisesE1) Convert to percentage:E2) Convert to integer or decimal, as appropriate:E3) A capital of R$ 8000 is invested for one year at a rate of 22\% p.a. (22\% per year).a) What is the interest?b) What is the amount?
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