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

Loan Amortization and EAR: You want to buy a car, and a local bank will lend you $40,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 8% with interest paid monthly. What will be the monthly loan payment? What will be the loan’s EAR?

Using a financial calculator: N=60, I/YR=8/12=0.6667, PV=-40,000, FV=0. Solve for PMT: $811.06.

To calculate the EAR: EAR = (1 + nominal rate/m)^m - 1. In this case, EAR = (1 + 0.08/12)^12 - 1.0 = (1.00667)^12 - 1.0 = 8.30%.

Loan Amortization Example: Jan sold her house on December 31 and took a $10,000 mortgage as part of the payment. The 10-year mortgage has a 10% nominal interest rate, with semiannual payments beginning next June 30. Next year, Jan must report... Continue reading "Understanding Loan Amortization and Calculating EAR" »

Vocabulary

English Definitions

Leading questions: Questions that encourage someone to answer in a certain way.

Mutually exclusive: Not able to be true or correct at the same time.

Weight: To give something more importance than something else.

Incentive: Something that will encourage people to do something.

Respondent: Person who completes a survey.

Analyse: To examine closely.

Ambiguity: When something has more than one possible meaning.

Jargon: Words used by one group of people, that other people might not understand.

Feedback: Opinions about something.

Dropout rate: The percentage of people who stop the survey before they have completed it.

Spanish Definitions

Liderar preguntas: Preguntas que animan a alguien a responder de cierta manera.

Mutuamente excluyentes:

Statistical Moments

A moment is a specific quantitative measure that characterizes a distribution. Two distributions are equal if their moments are equal.

Types of Moments:

• Related to the origin (0 as a reference)
• Related to the mean (μ as a reference)

M_r = (Σ(X_i – O)^r.n_i)/N

Where:

• X: individual observations
• r: Order of the moment (Order zero: r=0, First order: r=1, Second order: r=2, Third order: r=3)
• O: Origin or reference point
• n: frequency of each observation
• N: total number of observations

Properties:

• All moments of r=0 are equal to 1.
• Moments related to the mean are frequently called central moments.
• Moments with reference point 0 are frequently called ordinary moments.
• The arithmetic mean corresponds to the ordinary moment of the first order (r=

) Hypotheses, Type I and Type II Errors, and Statistical Tests

For each of the following tests, state the hypotheses, identify if it is a right-, left-, or two-tailed test and write Type I Error and Type II Error pertaining to the problem.

1. a) A professor of statistics states that the average student spends 3 hours studying for the midterm exam. Ho: μ = 3 vs. Ha: μ ≠ 3 Two-tailed test Type I Error: Concluding the average student doesn’t study 3 hours for midterm when in fact that is false. Type II Error: Not concluding the average student doesn’t study 3 hours for midterm when in fact that is true.
2. b) A spouse stated that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. Ho: μ = 1200 (or

Linear Programming

Linear Programming is an optimization technique useful for allocating scarce resources among competing demands.

Examples of LP Applications

• Selecting the product mix in a factory to make the best use of machine and labor hours available while maximizing the firm’s profit.
• Scheduling tellers at banks so that needs are met during each hour of the day while minimizing the total cost of labor.
• Determining food ingredient combinations that satisfy stated nutritional requirements at a minimum cost level.

Basic Concepts

• A single objective function states mathematically what is being maximized or minimized.
• Decision variables represent choices that the decision maker can control.
• Constraints are limitations that restrict the decision variables.

Golden circle:

This relates to the innovation. If a company is able to attract those who share its beliefs, it is also able to connect easier with innovators.

This is a graph made up of three circles, each inside the other. Each circle has a meaning and a way to apply it to our business efficiently.

We can explain the operation of the Golden Circle in such a way that while most companies ask themselves the answers to the question 'what' as their starting point, they are fully aware of the 'how', but very few companies are clear about the 'why'.

The 'what' responds to what we do and what we want to do. The 'how' responds to the processes through which we carry out our actions, and the 'why' would respond to the reason why we develop our business.... Continue reading "The Golden Circle: Driving Innovation and Quality Management" »

B. Changes in Inventories

The company must make an inventory of the stocks it has, doing a physical count of them and checking the result with the information recorded in the book balance. After verifying this data and correcting any differences, it is necessary to stabilize stock accounts; that is, to correct the accounting balance of these accounts to reflect reality.

C. Verification of Accounting Data

Before determining the result of the accounting fiscal year, the company must verify accounting data by checking, on the one hand, that there are no mistakes in arithmetic or transcription and, on the other, contrasting it with the economic reality. To do this, perform the following inventories and balances:

• Trial Balance: Its purpose is to check

International Accounting Standard No. 10

Events Occurring After the Balance Sheet Date

Objective

The objective of this Standard is to prescribe:

1. when an entity shall adjust its financial statements for events after the balance sheet date and
2. the disclosures that an entity should give about the date on which the financial statements were authorized for issue and about events after the balance sheet date.

The Standard also requires the entity that does not prepare its financial statements under the assumption of going concern, if the events after the balance sheet date indicate that this hypothesis of continuity is not appropriate.

Scope

This Standard is applicable in the accounting and disclosures related to events after the balance sheet date.

The events

Statistical Concepts