Money cannot guarantee happiness but grinding poverty can almost certainly guarantee misery. It is difficult to be happy when you know, in the back of your mind, that you are one small misfortune away from being unable to pay next month’s rent without resorting to payday lenders or the friendly neighborhood loan shark. Poverty is a complex topic and those of us who have never experienced it should not throw around simple platitudes regarding how to escape it. However, for a certain subset of those who find themselves in constant anxiety regarding money, the problem is almost certainly compounded by a lack of financial literacy.

#### Living on the Edge

According to a recent report, 66 million Americans have absolutely no savings available to cover a financial emergency. This shocking figure is nearly one-third of the roughly 206 million Americans between the ages of 15 and 64 which makes up the age group most likely to lack a safety net to deal with emergencies. A survey published by Standard & Poor’s revealed that only 57 percent of Americans are financially literate. Although it isn’t a good idea to unfairly stereotype individuals in large groups, it seems very likely that the Americans lacking savings also have a general lack of understanding of basic personal finance.

Why is this the case and what can be done about it?

One of the problems is that human beings do not seem to naturally understand non-linear systems, and this deficiency prevents us from automatically understanding what is perhaps the most important topic in personal finance: compound interest.

Here is one of the questions asked in the financial literacy survey:

Suppose you had $100 in a savings account and the bank adds 10% per year to the account. How much money would you have in the account after five years if you did not remove any money from the account: more than $150, exactly $150 or less than $150?

It is likely that most people would understand that 10 percent of $100 is $10 which represents the first year of interest. The account will be open for five years, so many people will be tempted to simply multiply the $10 by 5 and come up with $50 in total interest which is added to the initial $100 balance for a total of $150. However, this ignores the fact that you *earn interest on interest *which is the essence of compounding. Assuming annual compounding, the balance of the account would look like this over the five year span:

A simple formula can be used to determine the ending result of a sum invested at a certain rate over a certain period of time:

Ending Balance = Starting Balance * (1 + Periodic Interest Rate) ^ Number of Periods

The formula can be applied to this example as follows:

$161.05 = $100 * (1 + 0.1) ^ 5

Compound interest is an example of an *exponential equation *and the results do not neatly fit our natural intuitions. It is much more intuitive to think that the $100 deposit will earn $50 over five years than to figure out the actual result which is significantly more than $50. However, it is important to realize that this particular exponential function is very simple and should be understandable to the vast majority of people if explained clearly as part of a basic education.

#### The Longer View

To make the effect of compound interest more clear, let’s extend the period of time that the $100 is kept on deposit at a rate of 10%. Rather than assuming five years, let’s assume that the money is left alone for fifty years instead. If we apply the same “gut instinct” (but incorrect) logic that would have led someone to believe that the $100 deposit would only earn $50 over five years to this longer example, the answer would be that the fifty year deposit should earn a total of $500, which is 50 years multiplied by $10 per year.

Let’s see what the correct result is:

Ending Balance = Starting Balance * (1 + Periodic Interest Rate) ^ Number of Periods

This formula can be applied to this example as follows:

$11,739.09= $100 * (1 + 0.1) ^ 50

**Instead of earning the $500 that “gut instinct” might have led us to believe, the $100 deposit earns a shocking $11,639.09 in interest!**

This unintuitive result is due to the exponential nature of compound interest, as we can see from the graph below:

We can see that progress is slow at first, which we already knew based on the first five years of the investment. However, over time, earning interest on interest becomes the driving force behind the overall value of the account and we can really see the line start to explode upward over the second twenty-five year period.

#### What Applies to Savings Also Applies to Debt

How many people truly understand the horrible compounding effects of credit card debt? Although paying 15 to 20 percent interest on a $1,000 sofa might seem like an annoyance over the first year, making minimum monthly payments while taking on additional debt will cause the problem to snowball over time in just the same way that savings multiplied like crazy in the previous example. Actually, the snowball will be much worse. Compounding at 15 to 20 percent results in a much, much larger snowball than compounding at 10 percent.

Although credit card disclosure requirements have improved over the past several years and people are now clearly told how long it will take to retire debt based on minimum monthly payments, few people are going to pay much attention to the details on a credit card statement or stop using the credit card while paying it down.

#### Low Interest Rates Make Compounding Less Obvious

The example in the survey uses a rate of 10 percent for a savings account which is obviously unrealistic in today’s world of minuscule savings rates. However, low interest rates are probably not going to be a permanent phenomenon over the long run. The problem is that people have been trained to not appreciate the power of compound interest over the past several years because it is even less apparent than it otherwise would be.

Using a rate of 1 percent, which one would have been fortunate to get on a savings account over the past several years, the $100 deposit would have grown to only $105.10 over five years. In this case, the “intuitive” answer of believing that the total interest would be only $5 is hardly different from the correct answer of $5.10. In fact, it is so trivial that if we used the 1 percent rate in an example, people would laugh if we tried to claim that compound interest is actually important!

#### Multi-Disciplinary Education

Financial education is severely lacking in the United States and the fact that over half of Americans lack basic financial literacy is a national disgrace. The place to remedy the problem has to be the public school system. Ideally, parents would educate their children on personal finance but too many adults are financially illiterate themselves and we do not want to have a society where this perpetuates through multiple generations.

It should not be difficult to incorporate an appreciation for compound interest into the public school system. Basic exponential functions are routinely taught at the middle school level and, if not, certainly as part of a high school curriculum. Rather than using esoteric examples that students might not relate to, teachers could incorporate compound interest directly into basic math education covering exponential functions.

But is it the job of math teachers to cover personal finance? The better question is why not?

There need not be a special course in personal finance (although such an offering has obvious merits as well). Disciplines like mathematics should incorporate subject matter from other disciplines, particularly when doing so reinforces the math that is being taught. All young people are concerned with having enough money to spend. They might be too impulsive to care about long term growth of savings, but if they are at least aware of the potential of compound interest, that might prevent the accumulation of unwise debt in college or when starting out in the workforce.

Parents who are fully aware of the power of compound interest might try bypassing today’s low interest rate environment by setting up a family “bank” where their children can make “deposits” at rates that are far above market and possibly compound at a more frequent pace. For example, parents could offer their children an “account” that compounds at a rate of 5 percent every quarter. At that rate, a $100 deposit would grow to almost $150 over two years, well within the time frame that a teenager should appreciate.

#### Not a Panacea, But a Start

Even if every American left high school with a solid understanding of compound interest, we will still have people who fail to save because they lack self-control or fall into really hard times through no fault of their own. However, it is hard to believe that wide dissemination of this very basic principle would not dramatically reduce human misery. Not being able to cover the cost of a broken refrigerator, a tire blow-out, or a traffic ticket should be preventable for almost everyone.

There are enough truly difficult problems in life that do not lend themselves to simple solutions, so we should adopt simple ideas that have little or no downside such as teaching students about compound interest as part of their existing math programs. It might be overly optimistic to hope that all Americans will automatically think in terms of exponential functions rather than using their linear intuitions in everyday life. But when faced with major life decisions, the *default* should be to think in terms of compound interest when it comes to spending and saving money.