Suppose you notice that a country has average growth rate of 1% per year, while another grows 3% per year on average. At first glance, this may not seem a very big problem. What a difference 2% can do?
The answer is a big difference. Even growth rates that seem small, when written in terms of percentage, look great after you compose for many years.
Let''s consider an example. Suppose that two graduates - Jerry and Elaine - to achieve their first job at 22 years of age, earning 30,000 a year. Jerry lives in an economy where all incomes grow 1% annually, while Elaine lives in an economy where incomes grow at a rate of 3% per year. Just a few simple calculations to show what happens. Forty years later, when both have 62 years, Jerry will be earning $ 45,000 per year, while Elaine will be earning $ 98,000.Because of this difference of two percentage points in growth rate, the salary of Elaine will more than double that of Jerry.
An old rule of thumb, called the rule of 70 helps to understand the growth rates and the effects of the exponential function (compound interest). According to the rule 70, a variable grows at a rate of x% a year, then the variable double every 70 / x years or so. In Elaine economy, incomes grow 3% a year, so this will take about 70/3, or 23 years for incomes to double.
70 The rule applies not only to the growth of an economy, but also a savings account. Here''s an example: in 1791, Ben Franklin died and left $ 5 thousand to be invested for 200 years for the benefit of students of medicine and scientific research. If this money would yield 7% per annum (which would have been possible), the investment would double in value every ten years. After 200 years, would have doubled 20 times. At the end of 200 years of composition, the investment would be worth 220 x 5000, which is about $ 5 billion (in reality the 5000 Franklin only reached $ 2 million in 200 years because of the money was spent in the meantime .)