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Managerial Economics/Interest Calculations

Interest calculations are the relationship between time and money. For example, what's the difference between having $1,000,000 (1 million) now, versus having it a year later? If the money could have been received earlier and invested at 10%, then you would have had an additional 100,000 dollars the next year.

In a loan situation, you are taking money from the bank. This is money that you can spend now, so you are in effect, paying (paying the interest) to have this money on hand immediately. Conversely, when you invest, you are granting immediate money to another party, and they are paying you for this money, through interest.

In this section, we will be covering interest in depth and the different ways that interest can compound, and how it's calculated. In later sections we will cover cash flows such as payments in geometric and linear patterns.

Terminology

 * Principal
 * The initial money amount received in a loan or spent in an investment.

 * Interest Rate
 * The interest rate is the "cost" of the money, it is a percentage per period of time.

 * Interest Period
 * A measurement of the frequency that interest rate is applied to the current loan/investment. Typically Annually, Semi Annually, Quarterly or Monthly.

 * Annually
 * Interest is calculated once a year; Interest is usually calculated at the end of the year.

 * Semi Annually
 * The interest is calculated twice a year; Typically the interest will be calculated half-way through the year, and at the end of the year.

 * Quarterly
 * The interest is calculated 4 times a year, or every three months.

 * Monthly
 * Interest is applied at the end of every month.

Converting Interest Rates to different Interest Periods
Typically loans are given with a certain Annual interest rate, regardless of whether or not interest is calculated annually or not.

To convert from an interest period where interest is applied once, to a semi annually (were it's applied twice), the annual interest rate is converted to a semi annual interest rate.

This is best explained with an example. Suppose the annual interest rate is 10% and is to be applied semi-annually on a loan amount of $1000, then the interest is calculated as below:

The annual interest rate: 10% Number of semi-annual time periods in an year = 2 Therefore, semi-annual interest rate = 10/2 = 5%

Amount due at the end of the first half year = 1000*(1.05) = 1050

Amount due at the end of the second half year = 1050*(1.05) = 1102.50

Effectively you are halving the interest rate but multiplying it to to the amount twice.

Similarly, if the interest was to be applied on a quarterly basis then you would divide the annual interest rate by 4, but also multiply it to the amount 4 times.

In other words, if R is the annual interest rate, n is the number of time periods at which interest is applied then the effective rate E is given by

$$E = \left(1+\frac{R}{n}\right)^n$$

Bond equivalent yields (also called APR on most consumer loan documents) add these sub period rates to get an annual rate. The actual or effective rate compounds the interest according to the periods specified in the loan documents (normally continuous, daily, monthly, quarterly, semi-annually, or annually). To calc the effective rate you would add one to each of the period rates and multiply them together, then subtract one. If all your period rates are the same length and carry the same rate you can simplify the function to the form $$I=P*\left(\left(1+\frac{r}{n}\right)^n-1\right)$$

As an example for a quarterly 12% APR you have four compounding periods (each with 3% interest per period). Your effective rate is (1+0.03)^4-1 or 12.55% (rounded to two decimal places). As your n approaches infinity the formula changes to P*e^r where e is a constant that is approximately 2.71828 (it is irrational).

By convention different security types use different month and year assumptions. A few common assumptions are actual number of months/actual days in the year, 30 day months/360 day year, 30 day months/365 day year.

Simple Interest
Simple interest is where interest is calculated only of the principal. This will mean that the added amount of interest added during the interest period is constant throughout the duration of the transaction.

For example if I were to take a loan of 1000 dollars at 10% interest annually. At the end of each year I would owe an addition $100 dollars, regardless of however much the loan has shrunk.

Under simple interest the final amount due can be easily calculated

$$ I = (iP)N $$ Where I is the total interest due. P is the Principal. i is the interest rate. N is the number of times interest is applied. ie Number of Interest periods per year times number of years. The Final value of the transaction can be easily calculated under simple interest. Since the final value is the Principal plus the interest you get the following formula.

$$ F = P + I = P + iPN = P(1 + iN) $$ Where F is the final value. I is the total interest due. P is the Principal. i is the interest rate. N is the number of times interest is applied. ie Number of Interest periods per year times number of years. P = $1000 i = 10% N = 1 year

Calculation Simple Interest Formula $$ F = P (1 + iN) $$ $$ F = 1000 * (1 + (10/100) * 1) $$ $$ F = 1000 * 1.1 $$ $$ F = $1100 $$  Simple interest is less common than compound interest and is occasionally found in add-on loans or bonds.

Compound Interest
test Compound interest is denoted by the formula $$A = P(1 + i)^n $$

Inflation
http://www.economist.com/research/Economics/alphabetic.cfm?LETTER=I#INFLATION

Equivalence Calculations
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Economic History

When we think about economics, we often think about people on the floor of the stock exchange, trading millions of dollars' worth of shares each day. Or we think of board room meetings, where rich old men (and a lot fewer women) make decisions which end up making them richer. While it is true that this plays an important part in economics, it is not its most fundamental aspect. Economics is the study of how societies meet their needs, the most basic of which are food, clothing, and shelter; the elements necessary for survival. Once a society has met these needs, it can then look towards more luxurious items, education, health care, sports cars, personal aircraft; the list is mind-boggling.

To understand the highly complex economy in which we live at the moment, we first must see how it developed through the ages. It has been said that technology has driven economic development; indeed, a certain type of technology can be linked with new economic age. Human societies have a tendency to organise the way in which it runs, and meeting its own needs is no exception. Even in a household, there is usually some kind of system as to which chores are performed by which members of the household, which member(s) provide for the resources (in terms of income to buy food, clothing and shelter), and how much of that is saved or invested.

Hunter Gatherer Societies
The very first human societies were hunter-gatherers, that is, they hunted for and gathered their food. Clothing was obtained in the same way, and shelter was whatever people could find; caves and trees, perhaps. It should be noted though, even in such a primitive "economy", technology is necessary; basic stone-age tools such as clubs and spears allowed humans to hunt. Fire allowed humans to cook food which would otherwise be too difficult to eat, and also to ward off predators. In this society, there were really only three "occupations": hunters, carers and dependents. The hunters were mostly men, and were responsible for providing the food for the society, however some women were also gatherers; picking fruits and berries. Most of the women were carers; they looked after the fire and the society in making clothes, cooking, and caring for the dependents. Dependents were almost only children; people who could be neither hunters nor carers. Very few people lived to old age to require caring for, and those with disabilities were often left to die.

Agrarian Economy
The technological revolution which gave rise to the Agrarian Economy was domestication and farming. Until then, people could not decide what food they consumed; they had to eat whatever they could find. With farming, societies learned to control the types of products they would consume in a much more efficient way. Domesticating animals meant that meat; a food normally very difficult to come by; could now be obtained much more easily. As people no longer needed to roam about, they could afford to invest more resources into their dwellings; and correspondingly, houses became more sophisticated. Farming also brought humans closer together, and with the higher numbers of people, more needed to be organized. A very primitive form of labor division had begun; whereby people specialized in producing one commodity. Whereas before, a hunter was a hunter and a carer was a carer, now one could afford to grow only wheat, because he could trade it with someone else for meat, and so on. In some of these economies, a system of currency began to develop, however the most widespread method of trade was through barter.

Gift Economy
In the traditional form of commerce, goods are exchanged for goods deemed of equal value by the parties involved in the trade. In a gift economy, actors bestow lavish gifts upon others, not for a specific material return, but for the goodwill generated or status earned as a result.

Slave Labour
Slave labour was a key element in the development of many countries. It can be considered an economic system because it fulfills the needs of the society. However, the standard assumption of self ownership (see information on John Locke and others) is violated leading most to reject this system from principle. The slave-owners want to produce a certain commodity, and they do it through the cheapest way they can. They buy slaves and use them to produce their commodity, giving them no more than is necessary to protect their investment. When prices of slaves are cheap relative to the output from gang labor, this can amount to just enough to survive (food, clothing and shelter). In this way, slavery is profitable to the owners while the slaves live on less than they would demand if exchange were voluntary. It helped the investors to look for new forms of investing options. As they do not need to worry about the needs of the slaves. The positive effect of it is that it framed for the collectivity of wealth and for ideals of economic principles like mass production and reusability.

Feudalism
Feudalism is yet another economic system which is historically significant; in that it was the primary state of economy in much of the world for many hundreds of years. Feudalism is a hierarchical system where the majority of the labour power is dedicated to producing food; that being the peasants or serfs. A proportion of that produce is taken by the local nobility, that controls and governs by heritage the land and any peasants residing in it (Feudalism), or at times in a smaller scale to the lord of the manor usually holding his position in return for undertakings offered to a higher lord (Manorialism). These in return, provides the serfs with land to live on, shelter, and defense against external dangers. It is still an unjust system in that there is a highly wealthy class living next to an extremely poor class, but it was the standard way of life for many people throughout the Middle Ages.

Mercantilism
Mercantilism is an ideology that dominated post-Feudalism Europe, especially the colonial period. It was heavily based on protectionism, and promoted the acquiring of captive markets. This led to the colonial powers (England, Spain, France, etc.) that dominated the world stage for hundreds of years.

Industrial Economy
A direct result from the industrial revolution, that not only permitted the mass production of goods but the reduction of costs in the consumption of most goods that previously had to be hand crafted and limited in numbers. Most handcrafted production moved to luxury goods and the industrialization opened way to production many production methodology, the economy of scale, the production in series, to the just in time consumption in production resources.

A side result of industrialization was that labor also became less specialized and therefore less costly, as a trade-off energy prices and consumption increased and easy portable and accessible fuel gained importance.

Waste management and ecological considerations can also be seen as factors to consider when talking about industrial economy, as they have become a new factor in establishing cost when establishing an industrial economy.

Communist Economy
When the word "Communist" is used, it is often shrouded in fear and mystery and misunderstanding, especially in countries involved in the Cold War in particularly in the United States, that still is the primarily example for Capitalism. Put simply, it is an economic system where supposedly, economic decisions are made by the community as a whole; that is the entire community. However, most interpretations of the word or attempts to establish communism have ended up creating state-driven authoritarian economies and regimes which benefit single party political élite who are not accountable to the people at all.

Command Planned Economy

An economy characterized by Command Planning is notable for several distinguishing features. These are:

1. Collective or State Ownership of Capital:

Capital resources such as money, property and other physical assets are owned by the State. There is none (or very little) private ownership;

2. Inputs and Outputs are Determined by the State:

Typically, in a Command Planning economic system, the state has an elaborate planning mechanism in place which determines the level and proportions of inputs to be devoted to producing goods and services. Local planning authorities are handed 1 year, 5 year, 10 year or, in the case of China, up to 25 year plans. The local authorities then implement these plans by meeting with State Owned Enterprises, whereby, further plans are developed specific to the business. Inputs are allocated according to the plans, and, output targets are set;

3. Labor is allocated according to State Plans:

In a command planning economy there is no choice in whom you work for. From a very early age, when a child is in school, a streaming system allocates people into designated industries. If you test well at a young age you may be able to score a good job in an intellectual area, such as working in academia, or working for the bureaucracy - which in a command planning economy is massive as enormous organizational resources are needed to research, design and implement plans. If you are unlucky enough to test poorly when you are a young child, you may be streamed into working in an industry that is not to your liking, such as dull factory work, or basket weaving.

In this respect command planning differs substantially from free-market capitalism, such as countries like the USA, Canada, Australia, the United Kingdom and New Zealand (amongst others) experience. In such countries, there is no legal compulsion or government direction regarding a person's choice of employment. Irrespective of any government policy or directive, workers in free-market capitalist countries are free to compete with and against each other for jobs that are given based on the merits of the applicant. Additionally in this type of market, if a worker is unhappy with the particular line of work they are in, they are free to look elsewhere for employment. Workers are free to plan their own careers, switch jobs and careers as necessary to fulfill personal needs or goals, often using adult education to re-train for different careers.

4. Private Ownership is Not Possible:

Command Planning economies do not have any form of private ownership. Therefore, under a command planning system an individual cannot own shares, own real estate, or any other form of physical or non-physical asset. People are allocated residences by the State, and, this is usually done considering where and for whom you will be working for.

5. Prices and Paying for Goods and Services:

Prices are regulated entirely by the State, generally having only passing regard for the actual costs of production, but usually instead, having no regard for cost. Often a currency does not exist in a command planning economy, and, when it does its main purpose is for accounting.

Instead of paying for goods and services, as and when you need to buy them, you are allocated goods and services. This is often also called rationing.

In western democratic and capitalist societies the price mechanism is a fundamental operator in allocating resources. The laws of demand and supply interact, with the price of goods and services sending signals to producers and consumers alike as to what should be produced and in what quantities, and, what will be demanded and in what quantities.

The law of demand states that the higher the price of a good or service the less the amount of that good or service will be consumed. In other words, the quantity of a good or service demanded, rises when the price falls and, falls when the price increases.

Similarly, and in consequential opposition to the law of demand, the law of supply states that the higher the price of a good or service the greater the amount of that good or service, will be supplied to the market by a producer. In other words, a higher price attracts more producers to supply a greater amount to market.

This interaction occurs without any government intervention, and, in western democratic societies in which this system has operated for hundreds of years, it has been shown that the less government intervention, the greater the allocative efficiency of resources in the economy. This is not withstanding the need to enforce contracts in a functional legal system, uphold human and individual rights, and the provision of services and goods where the private market is unwilling or unable to supply, or, it simply isn't logical to supply in any other way.

6. Incentive Effects:

In a command planning economy there are none, if any, incentive effects to work harder, improve production techniques, and increase productivity and efficiency. In capitalist economic systems, it is this incentive to do well for ourselves, that generates harder work, creative solutions, enterprise, efficiency and productivity improvement.

It is not, therefore, incidental that it is this incentive effect that is responsible for the economic growth of the western world in the post world war II era, and the tremendous increase in standards of living that have been enjoyed by most of us in the western world.

Examples of the Types of Command Planning Economies:

The best example which springs to mind when thinking of command planning economic systems is the former USSR, known as the Soviet Union. North Korea in the present, modern-day era is perhaps another example, although this is a not-quite good enough case, as North Korea is heavily supported by the rest of the world - in particular China. China itself, used to be considered a Command Economy, however, in the 70s and 80s, and more dramatically in the 90's, China is generally considered to be Market Socialist in terms of its Economic Classification. They still have Socialist policies, but, markets do operate - apparently successfully enough to generate a surplus balance of trade with virtually every western country.

It is now generally thought that China's turn towards capitalism will make it the sole economic powerhouse of this century. This is happening because, unlike western economies, China is producing hundreds of thousands of very highly educated people in areas such as science, engineering and technology.

Cyber-Economy
As internet access spread into homes and businesses, more people communicated with each other around the world. These new interactions promoted new businesses and commercial relationships, and soon many existing businesses created their own spaces (webpages) online to advertise their products and services. Banking functions increased as security measures improved. Banks and businesses collaborated with software engineers to establish secure electronic commercial tools such as checkout systems, shopping carts, and auctions that offered safer online commerce. The amount and nature of business transactions expanded, and today this activity is called "e-commerce" or the "cyber economy".

The Creative Economy
The post-information age is giving rise to the creative economy, in which intrinsic human talents that cannot yet be duplicated by machines begin to dominate. In such an economy, the value of human labor lies in its creative output, rather than purely its productive output.

The Relationship Economy
An economic system in which one's personal connectivity and integrity determine their wealth, prosperity and success. Such a system is made possible by the internet and populism as a means of building a globally-connected consciousness and series of values.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Economic History


title: User:Vuara/VI.27