Compound Interest - Ms. Brown's Economics Classes
Compound Interest
Imagine that last year you invested $100 and receive a rate of return after one year of 10 percent, so that you have a gain of $10. You now invest your total, the $110, and receive a rate of return of 10 percent, but at the end of this year your gain is not $10, but rather $11. The rate of return hasn't changed, so why was the gain $10 last year and $11 this year? The answer is that when you reinvest past earnings, then in the future you will earn interest not only on the original investment, but also on the past accumulated returns; this is called compound interest.
The formula for compound interest, showing how much will accumulate by a certain time in the future given the original amount invested and the annual rate of return, is as follows:
Original investment(1 + rate of return)^number of years = future value
Thus, making a one-time investment of $1,000 and letting an 8 percent annual return on this investment compound for 40 years would give a future value of $1,000(1 + .08)^40 = $21,724. One lesson of compound interest is to try to save early to build lifetime wealth, because saving in your 20s and 30s allows much more time to accumulate and thus to let the power of compound interest work than saving done in your 50s or 60s.
A shortcut to finding out about how long it will take to double your money is called the Rule of 72. Divide the rate of interest you will be getting into 72. The answer will give you a ballpark figure on how long it will take for your money to double. A rate of eight percent will take about nine years to double the investment (72 divide by 8). Many students will think it would take about 12.5 years (100 divide by 8). The difference shows the power of compound interest.
Compounding can work for you or against you. If you save early and often, it works for you. If you borrow on a credit card and don't pay off the balance, it works against you.
Credit
Credit refers to the ability to borrow money. Some forms of credit commonly used by consumers are car loans, home mortgage loans and credit cards. Firms also use credit regularly, either by borrowing from a bank or issuing corporate bonds. Government also uses credit when it needs to borrow money to finance a budget deficit. Those who can borrow moderate or large sums of money at a reasonable rate of interest are sometimes said to have good credit, while those who cannot borrow such amounts at such rates are said to have bad credit.
Credit is extremely useful to the economy. Most people would have great difficulty in buying a house if they couldn't borrow the money. Many people also use credit to further their education. Many firms would be unable to build new factories if they had to save all the money first. In addition, short-term credit is often used by people (through credit cards) and firms as a simple and convenient method of paying for purchases.
However, excessive borrowing can be a problem for households, firms and government. Making interest payments because you borrowed money for the house that you live in, a car that you drive or a factory that produces goods can make good economic sense. But credit should not be used to pay for goods or consumption in the present that were completely consumed in the past. Be careful if the loan lasts longer than the item you bought with it.
Students often think that credit cards are money, and they don't recognize that there is a responsibility associated with credit. On a particularly beautiful day, allow your students to borrow 10 minutes of class time for additional free time. Explain that they will have to repay you later and that you will charge interest. On another particularly beautiful day, explain that the students will have to repay the time that they borrowed plus one minute. Reduce their free time by 11 minutes. They will complain, but remind them that credit involves borrowing something with the promise to repay. Discuss other things that they and other people borrow. Point out that when we borrow, we get something now, but we give up something in the future. Identify the extra minute as interest and explain that when people borrow money, they pay interest. Interest is the price paid for using someone else's money. Ask the students to analyze the costs and benefits of borrowing free time.
Credit can be an effective tool for purchasing goods and services that are needed or desired. When talking about credit, it is easy to only cite examples of the pitfalls of buying goods and services using credit. It is important to understand the positive aspects of establishing a good credit history. The ability to present a positive credit record is important to those seeking to borrow for business and personal needs in the future.
Like all of us, students have unlimited wants, and using credit seems like an easy way to fulfill more of them. How should students distinguish between good and poor uses of credit? One useful rule is to not finance anything for longer than its useful life. Borrowing for housing, automobiles and education makes more sense than borrowing for entertainment or the latest consumer products. Even borrowing to buy a car may not make sense if the loan is for a longer period than you expect to own the car.
Compare loans on the basis of the annual percentage rate (APR) and finance charge. Under the federal Truth in Lending Act, lenders must disclose these figures. Many people compare loans on the basis of the monthly payment. The monthly payment becomes lower if the repayment period is longer. Unfortunately, this also increases the finance charge. Avoid this confusion by determining the principal and repayment period first and then shop for the lowest APR.
When lenders are trying to determine whether a prospective borrower has "good credit" or "bad credit," they often look to what is commonly known as the "Three C's of Credit"--character, capacity and collateral. If all three C's are positive, that individual represents less of a credit risk to the lender and thus is more likely to receive credit.
Lenders and a growing list of others, such as employers, landlords and insurance providers, use a credit-scoring system to judge whether a prospective borrower, employee or renter is financially responsible. This credit score is called a FICO score. Credit scores are becoming a proxy for measuring character. Credit scores are based on information in credit reports. High credit scores are the result of keeping credit card balances low, paying bills on time and having steady employment. Low scores are associated with carrying high credit card balances, defaulting on payments and floating from job to job.
Financial Markets
Financial markets are those markets that exist for buying and selling financial assets. The most important financial assets for individual investors are bonds, stocks and mutual funds.
A bond is issued by a corporation or government as a way of borrowing money. An individual who purchases a bond gives money to the corporation or government that issued the bond, and in return, receives repayment of the money with interest over time. Short-term bonds are commonly repaid over a few months or a few years; long-term bonds are repaid over decades. Many bonds promise a fixed rate of interest. Investors in long-term bonds must be concerned that if inflation is unexpectedly high or nominal interest rates rise, they may be locked into a bond that pays an undesirably low rate of return.
A stock is a share of ownership in a business. If a firm has 100,000 shares of stock, and you own 1,000 shares, then you own 1 percent of the company. Owners of stock receive a return in two ways. The firm may pay dividends to its shareholders out of the profits that it earns. Also, investors may profit by selling their shares of stock for more than they paid for them; this is called a capital gain. However, if a company goes bankrupt, the stock is worth nothing. Thus, stocks are a riskier investment than many bonds.
Many individual investors want to diversify, that is, own a wide range of stocks and/or bonds from different firms and different levels of government, so that they don't have to worry too much about what happens with any individual firm. A mutual fund is an investment company that raises money from investors; purchases a range of stocks, bonds and other financial investments; and pays a return to shareholders according to the overall return of the entire fund. A mutual fund that seeks to mimic the average performance of the stock market as a whole is called an index fund. However, a mutual fund may focus on stocks or bonds from a particular industry or particular country or those that the mutual fund manager believes will perform well in the future. For many individual investors, it is much easier to diversify by using one or a few mutual funds, than by purchasing dozens or hundreds of individual stocks and bonds.
We hear all the time that the market did this or the market did that today. Actually, there is no one market or even one index that represents the market. There are markets for millions of stocks, bonds and other financial instruments. In the words of Warren Buffett, "the stock market doesn't exist. It is only there as a reference to see if anyone is doing anything foolish."
Many people want to "beat the market." Most evidence, however, shows that it is very difficult for investors to beat market averages although constructing a diversified portfolio of index funds or exchange-traded funds can be a science in itself. Mark Twain said, "There are two times in a man's life when he should not speculate: when he can't afford it and when he can."
People often view financial markets as a financial casino with winners and losers. Financial markets are much more important than that and are critical to a successful economy. Financial markets and financial institutions channel savings and financial investments into real investments such as new factories and machines. Financial markets also channel money from savers to borrowers, enabling them to buy homes and other durable goods. Without financial markets, economic growth and prosperity would suffer.
Insurance
The purchase of insurance involves paying an amount called a premium at regular intervals, with the understanding that if negative events occur, the insurance company will pay certain costs. For example, health insurance provides payments to health-care providers if you are sick. Life insurance provides a payment to your descendants if you die. Car insurance provides payments for damages caused in an auto accident. Homeowner's insurance pays for home repairs in the case of fire or storm damage.
Insurance works on the principle that in a large group of people historical experience allows one to predict with some accuracy how many of them will suffer a negative event each year--but no one can say in advance exactly who in the group will suffer the negative events. Individuals who are averse to taking risks prefer to pay an insurance premium, and be protected against the high costs of negative events, instead of waiting to find out if they are unlucky enough to suffer the negative events. The great irony of insurance is that it is a purchase one hopes never to benefit from--since that would mean that the negative event has occurred.
Explain to your students that the purpose of insurance is to share risk. You don't buy insurance to make money, but instead to guard against loss. Therefore, buying insurance makes the most sense when the potential loss is great and there is a significant probability of loss over the long term. It does not make sense to insure against losses that are small or that will definitely happen because risk does not have to be shared in these circumstances.
Many students will be approached about buying life insurance when they graduate. You might understand the concept better if it were called "death insurance" because the main purpose of life insurance is to replace lost income if a family's wage earner dies. When you view life insurance in this way, you will understand that they don't need much of it yet.
Risk and return
Risk describes a situation in which the outcome is uncertain and a range of results, potentially both good and bad, is possible. The greater the range of possible outcomes, the greater the risk. For example, imagine two investment strategies, both with the same cost. The first strategy has a one-third chance of making profits of $9 million, a one-third chance of making profits of $10 million and a one-third chance of making profits of $11 million. The second strategy has a one-third chance of making losses of $5 million, a one-third chance of making profits of $10 million and a one-third chance of making profits of $25 million. In both cases, the average or expected outcome is $10 million. But the first strategy has less risk, because the range of possible outcomes is grouped more closely together.
The return of an investment is calculated as the income or profit generated by that investment divided by the original cost of the investment. The rate of return is usually expressed as a percentage over a year. If you put money in a bank account and receive a 3 percent rate of interest, then the return is 3 percent. A more complex example would be if you invest money in a stock which pays a dividend and also increases in value per share. The total increase in value, including both dividend and the rise in the share price, would be counted in the rate of return. Firms need to make projections about rate of return when they make decisions about building a new plant, buying a large piece of equipment or launching a new product. They calculate the additional profit that they expect to earn from the business decision, divided by the cost of that decision.
There is a strong relationship between risk and return. Generally, the greater the risk, the higher the potential return. If an investment seems too good to be true, it probably is.
Drive home the risk and return trade-off by asking the students to evaluate the old investment cliché, "If an investment seems too good to be true, it probably is." What does this mean in terms of risk and return?
Saving and investing
Broadly speaking, an individual has only two choices about what to do with (after-tax) income: spending on current consumption or saving for the future.
From an individual point of view, saved money typically becomes a form of investing, since the money is put into a bank account, stock, bond or mutual fund that pays a rate of return. For an individual, investing refers to postponing current consumption or rewards to pursue an activity with expectations of greater benefits in the future. Financial investment refers to the decisions by individuals and firms to invest money in financial assets such as bank accounts, certificates of deposit, stocks, bonds and mutual funds. Financial investment is crucial to accumulating personal wealth.
Real investment or physical capital investment is the component of aggregate demand that refers to the decisions by firms to purchase equipment and physical plant, and also the purchases of new homes by consumers. The amount of real investment is critical to economic growth. Financial investment and real investment are connected, but they are not the same. Thus, when you hear a casual reference to "investment," be clear in your own mind on whether it is financial investment or real investment.
Households: Individuals and family units that buy goods and services (as consumers) and sell or rent productive resources (as resource owners).
Save: To keep money for future use; to divert money from current spending to a savings account or another form of investment.
Interest: Money paid regularly, at a particular rate, for the use of borrowed money.
Money: Anything that is generally accepted as final payment for goods and services; serves as a medium of exchange, a store of value and a standard of value. Characteristics of money are portability, stability in value, uniformity, durability and acceptance.
Budget: A spending-and-savings plan, based on estimated income and expenses for an individual or an organization, covering a specific time period.
Bond: A certificate of indebtedness issued by a government or a publicly held corporation, promising to repay borrowed money to the lender at a fixed rate of interest and at a specified time.
Bank: A financial institution that provides various products and services to its customers, including checking and savings accounts, loans and currency exchange.
Credit Card: A small, specially coded plastic card issued by a bank, business, etc., authorizing the cardholder to purchase goods or services on credit.
Mortgage: A special type of loan for the purchase of a house or other real estate.
Consumers: People who use goods and services to satisfy their personal needs and not for resale or in the production of other goods and services.
Credit: The opportunity to borrow money or to receive goods or services in return for a promise to pay later.
Investing: The process of putting money someplace with the intention of making a financial gain. Investment possibilities include stocks, bonds, mutual funds, real estate, and other financial instruments or ventures.
Compound Interest: Interest that is earned not only on the principal but also on the interest already earned.
Rate of Return: Earnings from an investment, stated as a percentage of the amount invested; usually calculated on an annual basis.
Stock Market: A market in which the public trades stock that someone already owns; buying and selling of stock.
Index Fund: A mutual fund whose objective is to match the composite investment performance of a large group of stocks or bonds such as those represented by the Standard & Poor's 500 Composite Stock Index.
Risk: The chance of losing money.
Capital Gain: A profit realized from the sale of property, stocks or other investments.
Dividend: A share of a company's net profits paid to stockholders.
Profit: Income received for entrepreneurial skills and risk taking, calculated by subtracting all of a firm's explicit and implicit costs from its total revenues.
Return: Earnings from an investment, usually expressed as an annual percentage.
Inflation: A rise in the general or average price level of all the goods and services produced in an economy. Can be caused by pressure from the demand side of the market (demand-pull inflation) or pressure from the supply side of the market (cost-push inflation).
Borrow: To receive and use something belonging to somebody else, with the intention of returning or repaying it--often with interest in the case of borrowed money.
Corporation: A legal entity owned by shareholders whose liability for the firm's losses is limited to the value of the stock they own.
Bond: A certificate of indebtedness issued by a government or a publicly held corporation, promising to repay borrowed money to the lender at a fixed rate of interest and at a specified time.
Mutual Fund: A pool of money used by a company to purchase a variety of stocks, bonds or money market instruments. Provides diversification and professional management for investors.
Stock: An ownership share or shares of ownership in a corporation.
Asset: Something of monetary value owned by an individual or an organization.
Markets: Places, institutions or technological arrangements where or by means of which goods or services are exchanged. Also, set of all sale and purchase transactions that affect the price of some good or service.
Economic Growth: An increase in real output as measured by real GDP or per capita real GDP.
Productivity: Amount of output (goods and services) produced per unit of input (productive resources) used.
Income: Payments earned by households for selling or renting their productive resources. May include salaries, wages, interest and dividends.
Wage: Payments for labor services that are directly tied to time worked, or to number of units of output produced.
Human Capital: The health, education, experience, training, skills and values of people. Also known as human resources.
Benefit: Monetary or non-monetary gain received because of an action taken or a decision made.
Risk: The chance of losing money.
Costs: An amount that must be paid or spent to buy or obtain something. The effort, loss or sacrifice necessary to achieve or obtain something.
Premium: The fee paid for insurance protection.
Insurance: A practice or arrangement whereby a company provides a guarantee of compensation for specified forms of loss, damage, injury or death. People obtain such guarantees by buying insurance policies, for which they pay premiums. The process allows for spreading out of risk over a pool of insurance policyholders, with the expectation that only a few policyholders will actually experience losses for which claims must be made. Types of insurance include automobile, health, renter's, homeowner's, disability & life.
Bank Account: An arrangement by which a bank holds funds on behalf of a depositor. Also, the balance of funds held under such an arrangement, credited to and subject to withdrawal by the depositor.
Rate of Return: Earnings from an investment, stated as a percentage of the amount invested; usually calculated on an annual basis.
Investment: The purchase of capital goods (including machinery, technology or new buildings) that are used to produce goods and services. In personal finance, the amount of money invested in stocks, bonds, mutual funds and other investment instruments.
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