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Economic growth is tied closely to how well people live. We already saw how a high growth rate in China changed the lives of much of its population—more people now can buy cars, computers, and other goods that previously were either unavailable or unaffordable. Economic growth improves the lives of people of all income levels, from the richest to the poorest citizens.

The benefits of economic growth extend beyond the goods people can buy. For example, economic growth leads to lower poverty rates and longer life expectancies as people can afford better medical care, more nutritious diets, and more leisure to reduce stress. The data speak for themselves. In 1980 the average life expectancies (females and males combined) in China and India were 67 and 54 years, respectively. In 2016 they were 75 and 68 years, respectively. Children born in China and India today can expect to live about a decade longer, on average, than their parents.

Still, according to estimates by the World Bank, over a billion people in the world live on less than $1.25 per day, and over 2 billion people live on less than $2 per day. However, the number of people living on these amounts has fallen from their peaks as many countries, such as the BRIC nations which make up over 40% of the world’s population, saw economic growth rates improve over the past two decades. This section analyzes how economic growth is measured and how the power of compounding, in which growth builds upon prior growth, can turn small rates of growth into substantial increases in outcome and income over time, leading to better lives for all.

Small differences in growth can lead to dramatic differences in income due to the effect of compounding. To show this, we first have to measure economic growth, using the concepts of gross domestic product (GDP) and GDP per capita introduced in an earlier chapter. As we saw, GDP is a measure of the total value of final goods and services produced in a country in one year, or simply a country’s total annual output. GDP per capita is a country’s GDP divided by its population, and provides a rough measure of a typical person’s standard of living. Also, recall that real GDP and real GDP per capita use constant dollars to remove the effects of inflation, allowing for more accurate comparisons in output from year to year.

When a country’s real GDP per capita increases, the average output per person is increasing (rather than just prices), and this generally translates into a higher standard of living for most of its residents. Therefore, this is a good indicator of how an economy grows over time.

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In the United States, real GDP is measured by the Bureau of Economic Analysis (BEA). The BEA produces quarterly reports on the changes in U.S. GDP from the previous quarter, and is reported as an annualized rate (quarterly change multiplied by 4). For example, in January 2016, the BEA reported that the U.S. economy grew 0.7% in the fourth quarter of 2015. This means that real GDP in the United States increased 0.175% from the third quarter of 2015 to the fourth quarter of 2015, which equals a rise of 0.7% when annualized.

In addition, the BEA provides GDP growth data year-over-year. For example, the BEA reported that the U.S. economy grew 1.8% from the fourth quarter of 2014 to the fourth quarter of 2015. Why does the BEA report year-over-year growth? Year-over-year growth allows investors and policymakers to compare how the economy has grown over an entire 12-month period, without the seasonal ups and downs most economies experience. Table 1 shows the quarterly real GDP growth rates in 2015 using the annualized and year-over-year methods. The Annualized column shows the seasonal fluctuations that influenced economic growth each quarter, while the Year-Over-Year column shows the growth rate for the preceding 12 months. Both measures are useful depending on whether one is analyzing trends in economic performance for a particular season or for the entire year.

Data from BEA Interactive Tables: GDP and the National Income and Product Accounts.

When we think of a stark contrast in living standards, we need look no further than the U.S.–Mexican border. For example, driving along Interstate 10 in El Paso, Texas (which is less than 200 yards from the border at its closest point), one can see tremendous differences in the quality of housing in Mexico versus that in the United States. Yet, how did such a difference in standard of living occur? Did the U.S. economy grow that much faster? The surprising answer is that the U.S. growth rate over the past 100 years averaged just 1% higher than Mexico’s growth rate. Perhaps more surprising is that Mexico’s real GDP per capita is above average in the world. Even Mexico appears “rich” to countries such as Nicaragua and Honduras, whose real GDP per capita is only about one-fourth that of Mexico. If growth rates did not differ much between the United States and Mexico, or between Mexico and Nicaragua over the past century, why are the economies of these countries so different? The answer is the power of compounding growth.

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Power of Compounding Growth Rates Suppose you deposit $1,000 in a high-interest money market account that averages 10% in interest per year. If you simply let the interest accrue without adding any additional money to the account, that $1,000 would turn into $28,102 in 35 years. How is that possible? Money earns interest, in this case 10%. But interest also earns interest. In fact, jump ahead 34 years, when your $1,000 is worth $25,548. In year 35, earning 10% on $25,548 equals over $2,500 in interest, bringing your total to $28,102. In that year, you earned over 2.5 times more in interest than the $1,000 you originally put in. That is the power of compounding growth.

Suppose instead that your money grew at 5% per year. What do you think the return will be? One-half of the 10% amount of $28,102? No . . . saving $1,000 at 5% would result in a total value of $5,516 in 35 years, significantly less than half of the $28,102 had the interest rate been 10%. This example shows that small differences in interest result in big changes over time. Suppose that your money grew at 9%, just 1% less than 10%. Your $1,000 would be worth $20,414 in 35 years, a drop of almost $8,000 over this period.

These numerical examples highlight the importance of small differences in growth between the United States and Mexico over time. By growing just 1% faster over a 100-year period, two countries can end up having real GDP per capita several times apart (about 4 times in the case of the United States and Mexico and about 4 times between Mexico and Nicaragua). Over the past 100 years, the United States grew 2% a year on average, Mexico grew 1.2% a year on average, and Nicaragua grew 0.3% a year on average.

Rule of 70 Calculating compounding growth over a long period requires the use of a formula and calculator. Luckily, there is an easy way to approximate the number of years it takes for an amount to double in value by using the Rule of 70. The Rule of 70 states that the number of years required for a value (such as a nation’s GDP) to double in size is equal to 70 divided by the growth rate:

Number of Years to Double Value = 70/Growth Rate

For example, if the growth rate is 10%, it would take about 70/10 = 7 years for an initial value of $1,000 to double to $2,000, another 7 years (or 14 years total) to double again to $4,000, another 7 years (or 21 years total) to double again to $8,000, and so on.

The Rule of 70 is fairly accurate for small growth rates. For larger growth rates, especially above 10%, the Rule of 70 becomes slightly less accurate over time. Table 2 provides a comparison between actual values and estimated values using the Rule of 70 for 5% and 10% growth rates. The smaller growth rate keeps the Rule of 70 estimated values closer to the actual values than the larger growth rate.

Although the Rule of 70 does not provide an exact estimate of compounded values over time, its ease of use makes it a valuable tool in understanding the power of compounding growth rates over time.

In all examples so far, we have shown how compounding growth can lead to much improved lives over time. However, it is also important to note that the reverse can be true. The compounding effect also makes debts significantly larger over time.

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Do you keep a balance on a credit card? If so, you’re not alone. The average American household carries about $16,000 in credit card balances each month. Most credit cards charge interest rates on unpaid balances between 12% and 18%, some even more. Suppose an individual has $15,000 in debt at a 17.5% interest rate. If no payments are made on this debt (let’s assume a minimum monthly payment is not required), the Rule of 70 says that the debt will double about every 4 years (70/17.5). If no payments are made on this debt, that $16,000 will turn into $32,000 in 4 years, $64,000 in 8 years, $128,000 in 12 years, and $256,000 in 16 years. Paying off credit card balances can lead to significant savings over time.

In sum, the power of compounding means that policies aimed at increasing the annual rate of economic growth can have powerful long-run effects, resulting in some countries becoming rich while others that do not achieve such growth remain poor. The benefits of economic growth are highlighted through the remarkable rise in income over time that leads to a higher standard of living for all citizens. But what exactly spurs economic growth? That is a question we answer in the next section.

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