Notes, summaries, assignments, exams, and problems for Mathematics

Forward Rate Agreement (FRA)

A Forward Rate Agreement (FRA) is a contract between two parties who wish to protect themselves against fluctuating interest rates. These are over-the-counter (OTC) contracts, meaning they are not traded on organized exchanges, and are considered off-balance-sheet items because there is no exchange of the principal amount.

It is a contract whereby two parties agree on an interest rate for a specific notional amount for a specific period at a future date. There is no intention, obligation, or commitment to exchange the principal, which is why it is qualified as theoretical or notional. An FRA is a bilateral contract that allows parties to set the terms of a loan (amount and interest rate) to be taken or granted at... Continue reading "Forward Rate Agreements (FRAs) and Interest Rate Swaps Explained" »

Accounting Fundamentals

Accounting is defined as the science that informs traders of the composition of their assets, as well as operations that modify them, using specific books and accounting records. Its purpose is to provide an economic and financial rating of a company.

Objectives of Accounting

• Financial Situation: Inform the economic and financial situation of the company and its patrimony. This data is collected through inventory balances and, more recently, the statement of changes in net equity.
• Performance Reporting: Report the results of losses or gains obtained during the development of the company's financial activities, typically shown through the profit and loss account.
• Contextual Analysis: Report the causes behind these results

This analysis delves into the financial performance of the company for the years 2007 and 2008, focusing on key liquidity and operational efficiency metrics such as working capital and various maturity periods.

Working Capital Calculation (2007-2008)

The working capital is calculated as the difference between current assets and current liabilities. Here are the results for 2007 and 2008:

• 2008: Current Assets (2,788,286) - Current Liabilities (3,020,313) = -232,027
• 2007: Current Assets (2,741,769) - Current Liabilities (2,953,480) = -211,711

Both periods show negative working capital. This indicates that the company's current liabilities exceed its current assets. The negative working capital remained almost constant across both years.

Analysis of

Business Cycles

Long Cycle

The long cycle begins with fundraising and the immobilization of capital in fixed assets. The annual amortization cost is incorporated into the product, which allows for the recovery of a portion of the annual investment. When assets are fully depreciated, the depreciation funds are used to renew them, leading to another cycle. The company recovers the money that was immobilized through depreciation.

Scheme:
+ Own resources / Outside resources → Money → Investment → Depreciation → Money

Short Cycle

Also called the cycle of operation, the business cycle, or the money-goods-money cycle. It starts with the immobilization of resources in the acquisition of raw materials, continues with production, marketing, and the... Continue reading "Understanding Business Cycles and Maturation Periods" »

Linear Equations

First-degree algebraic expressions with several unknowns.

Linear equations with 2 unknowns correspond to the general equation: ax + by = c

Solution of a Linear Equation

A solution is any pair of values for the unknowns that verifies the equation.

If x1, y1 are real numbers, the pair (x1, y1) is a solution of the linear equation in two unknowns if: ax1 + by1 = c.

Linear equations with 2 unknowns have infinite solutions.

Graphical Representation

The equation ax + by = c is a straight line. Each point on this line is a solution of the equation.

Systems of Linear Equations

A linear system of two linear equations with two unknowns is an algebraic expression of the form:

ax + by = c
a'x + b'y = c'

Solution of a System

A solution is any pair of... Continue reading "Solving Linear Equations and Systems" »

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Matrix Fundamentals

A matrix is a rectangular array of elements arranged in rows and columns, having no numerical value in themselves. Matrices are denoted with capital letters, and their elements are represented by lowercase letters.

Types of Matrices

• Diagonal Matrix: A square matrix where all elements are 0 except those on the main diagonal.
• Scalar Matrix: A square matrix where all elements are 0 except those on the main diagonal, which are equal.
• Unit (Identity) Matrix: A square matrix where all elements are 0 except those on the main diagonal, which are equal to 1.
• Lower Triangular Matrix: A square matrix where all elements a_ij with i < j are equal to 0.
• Upper Triangular Matrix: A square matrix where all elements a_ij with i > j are equal

Organizational Design Variables and Work Structure

Structural Differentiation (Item 6 Continued)

Horizontal differentiation relates to the division of labor and the number of units and tasks. The grouping of tasks defines the structure.

Vertical differentiation relates to the number of posts and reflects the division of labor, giving rise to structures such as tall and flat structures. Spatial differentiation is a conglomerate of the two previous types.

Formalization and Centralization

Formalization ensures people's behavior and the way tasks are performed, aiming for the correct execution. This is achieved through:

• Establishing rules.
• Procedures design.
• Process design.

Centralization and standardization relate to the distribution of powers and responsibilities... Continue reading "Organizational Structure and Behavioral Design Variables" »

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SQL Date Format Cheat Sheet

This reference provides a comprehensive list of SQL Server CONVERT styles for formatting date and time values. Use these codes to transform your data into the desired output format.

Common Date and Time Conversion Styles