Different types of growth patterns can yield drastically different results, even though the stated growth rates are the same. That's because the formula to calculate simple growth is different than the formula for compound growth, which is also known as exponential growth.
Simple growth doesn't account for any increases between the time the growth starts and the time the growth ends. To calculate simple growth, multiply the original amount by the growth rate by the time over which the growth occurs. For example, if you start with $100 and it grows by 4 percent per year for three years, multiply $100 by 0.04 by 3 to find the balance grows by $12.
Compound growth, on the other hand, accounts for growth being added throughout the time the growth occurs. How often the growth gets added is known as the "compounding period." For example, if a bank compounds interest on your account annually over a three year period, that means the interest from the first year is added at the end of the year and then that interest begins accruing addition interest for the next two years.
To figure the growth, add 1 to the growth rate per period, raise the result to the power of the number of compounding periods, subtract 1, and then multiply by the initial amount. For example, if you start with $100 and it grows by 4 percent per year for three years, add 1 to 0.04 to get 1.04, raise 1.04 to the third power to get 1.125, subtract 1 from 1.125 to get 0.125, and multiply 0.125 by $100 to find the balance grows by $12.50, slightly more than if you use the simple growth formula.