43. Financial Mathematics

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Financial Mathematics is one of the subjects that make up the syllabus of Mathematics for the Enem test. This course's main objective is to provide the student with a solid understanding of the basic principles of financial mathematics and how they are applied in a variety of financial situations.

To begin with, it is important to understand the concept of interest. Interest is the fee charged for borrowing money (or another item) for a certain period of time. There are two main types of interest: simple and compound. Simple interest is calculated on the principal amount only, while compound interest is calculated on both the principal amount and accrued interest from previous periods.

The formula for calculating simple interest is J = P * i * n, where J is the interest, P is the principal (initial amount), i is the interest rate, and n is the number of periods. The formula to calculate compound interest is A = P * (1 + i)^n, where A is the final amount (principal + interest), P is the principal, i is the interest rate, and n is the number of periods .

Another important concept in financial mathematics is discounting. The discount is the difference between the future value of a payment and its present value. There are two main types of discounts: simple and compound. The simple discount is calculated on the future value, while the compound discount is calculated on the present value.

The formula for calculating the simple discount is D = F * d * n, where D is the discount, F is the future value, d is the discount rate, and n is the number of periods. The formula to calculate the compound discount is D = F * (1 - (1 / (1 + d)^n)), where D is the discount, F is the future value, d is the discount rate and n is the number of periods.

Financial mathematics also addresses the concept of amortization, which is the process of paying off a debt over time through regular payments. The amortization table is a useful tool that shows the payment for each period, the amount of interest paid, the amount of principal paid, and the remaining outstanding balance.

There are several amortization methods, including the constant amortization system (SAC), the French amortization system (SAF), and the American amortization system (SAM). Each of these systems has its own characteristics and is suitable for different types of loans and financial situations.

Finally, financial mathematics also deals with the concept of the equivalent interest rate, which is the interest rate that makes two different cash flows equivalent in terms of present value. Equivalent interest rate is useful for comparing different investment or financing options.

In summary, financial mathematics is an essential discipline for anyone who wants to perform well in the Enem test. It provides the tools you need to understand and analyze a variety of financial situations, from calculating interest and discounts to paying off debt and comparing different investment options.

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