MTH001 Final Term Subjective

MTH001 Elementary Mathematics FAQs For Final

Term Exam Preparation

FAQs Question: What is interest?

Answer: Interest is the cost of borrowing money. An interest rate is the cost stated as a percent of the amount borrowed per period of time, usually one year. The prevailing market rate is composed of: 1. The Real Rate of Interest that compensates lenders for postponing their own spending during the term of the loan. 2. An Inflation Premium to offset the possibility that inflation may erode the value of the money during the term of the loan. A unit of money (dollar, peso, etc) will purchase progressively fewer goods and services during a period of inflation, so the lender must increase the interest rate to compensate for that loss.. 3. Various Risk Premiums to compensate the lender for risky loans such as those that are unsecured made to borrowers with questionable credit ratings, or illiquid loans that the lender may not be able to readily resell. Question: What is simple interest?

Answer: Simple interest is calculated on the original principal only. Accumulated interest from prior periods is not used in calculations for the following periods. Simple interest is normally used for a single period of less than a year, such as 30 or 60 days. Simple interest = p * i * n where: p = principal (original amount borrowed or loaned) i = interest rate for one period n = number of periods Question: What is compound Interest?

Answer: Compound interest is calculated each period on the original principal and all interest accumulated during past periods. Although the interest may be stated as a yearly rate, the compounding periods can be yearly, semiannually, quarterly, or even continuously. You can think of compound interest as a series of back-to-back simple interest contracts. The interest earned in each period is added to the principal of the previous period to become the principal for the next period. For example, you borrow $10,000 for three years at 5% annual interest compounded annually. Question: What is Present Value?

Answer: Present Value is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate. Since money has time value, the present value of a promised future amount is worth less the longer you have to wait to receive it. The difference between the two depends on the number of compounding periods involved and the interest (discount) rate. PV = FV [ 1 / (1 + i)n ] Where: PV = Present Value FV = Future Value i = Interest Rate Per Period n = Number of Compounding Periods Question: What is Future Value?

Answer: Future Value is the amount of money that an investment made today (the present value) will grow to by some future date. Since money has time value, we naturally expect the future value to be greater than the present value. The difference between the two depends on the number of compounding periods involved and the going interest rate. FV = PV (1 + i)n Where: FV = Future Value PV = Present Value i = Interest Rate per Period n = Number of Compounding Periods Question: What is Accumulated Value?

Answer: What your money is worth after it earns interest, dividends, or capital gains. Includes the amount you started with, plus any increase. Question: How to solve linear equations?

Answer: The most important consideration with equations: No matter what kind of equation you're dealing with -- linear or otherwise -- whatever you do to the one side, you must do the exact same thing to the other side! Equations are like toddlers in this respect: You have to be totally, totally fair! Whatever you do to an equation, do the S A M E thing to B O T H sides of that equation! Question: What are the basic algebraic operations?

Answer: We can say that the “basic” algebraic operations you must master are: addition (of two or more terms or expressions) • subtraction (of one term or expression from another) • multiplication (of one term or expression by another) In the case of multiplication, it turns out to be useful not only to start with two expressions and be able to write down the result of multiplying them together, but also, to be able to start with an expression and rewrite it as the product of two or more factors. • division (of one term or expression by another – this leads to the whole subject of working with fractions containing literal symbols.) • manipulating radicals or roots, particularly square roots, of algebraic expressions Question: What is ratio?

Answer: A ratio is a comparison of two numbers. We generally separate the two numbers in the ratio with a colon (:). Suppose we want to write the ratio of 8 and 12. We can write this as 8:12 or as a fraction 8/12, and we say the ratio is eight to twelve.

Question: What is proportion?

Answer: A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal. 3/4 = 6/8 is an example of a proportion. Question: What is rate?

Answer: A rate is a ratio that expresses how long it takes to do something, such as traveling a certain distance. To walk 3 kilometers in one hour is to walk at the rate of 3 km/h. The fraction expressing a rate has units of distance in the numerator and units of time in the denominator. Question: What is statistics?

Answer: Statistics as a discipline is the development and application of methods to collect, analyze and interpret data. Modern statistical methods involve the design and analysis of experiments and surveys, the quantification of biological, social and scientific phenomenon and the application of statistical principles to understand more about the world around us. Question: Is statistics hard?

Answer: No! Questions like this invariably lead to self-fulfilling prophecies. Tell yourself statistics is hard, and it's hard. Tell yourself statistics is easy, and it's easy! As with most activities rich enough to demand formal study, there are traps for the unwary that must be avoided. Fall into them at the beginning, and statistics is hard Avoid them from the outset, and you'll wonder what the fuss is all about. The amount of success and the speed with which you'll achieved it depend in large part on how quickly these particular lessons are learned. 1. Statistics is as much about philosophy as about anything else. There are many ways to analyze data. The two major camps split themselves into frequentists and Bayesians, but there are many flavors of each as well as other camps, such as the decisiontheorists and those who favor the likelihood approach. The reason for these different approaches has to do with questions like, " What is the probability that a particular theory is true?" Bayesians will answer that question with a number. Frequentists will say that the question is meaningless. The theory is either true or not. It can be a worthwhile exercise to spend a few minutes (hours, years, professional lifetimes,...) considering what is meant by "the probability that a theory is true". Problems ensue when people forget about what is allowed under what system and try making statements about the probability of something being true while conducting a frequentist analysis. 2. Statistics is backwards! One thing most people (even statisticians!) would like to do is describe how likely a theory or hypothesis might be in light of a particular set of data. This is not possible in the commonly used classical/frequentist approach to statistics, which is the approach taken in these notes. Instead, statistics talks about the probability of observing particular sets of data, assuming a theory holds. We are not allowed to say, " Because I've seen these data, there is only a small probability that this theory is true." Instead, we say, " The probability of seeing data like these is very small if the theory is true." This means we need methods for translating this latter type of statement into a declaration that a theory is true or false. As a result... Statistical