What is the magic or power of compounding? This simply refers to an investment that is left to keep appreciating in value (rather than being cashed in or having its dividends or capital gains sent to the investor), so that, for example, an asset that goes up 10% a year, left fully invested, is then worth 110% of the original amount at the end of the first year, all 110% of which is receiving 10% through the second year, etc. Thus over time a higher and higher percentage of the original investment is appreciating.
In this example, it would take about 7 years for the compounded appreciation to double one's investment, whereas with simple interest, 10% sent to the investor as a dividend each year for example, a decade would be required to get back the original investment amount or have twice as much.
If a person begins tax-deferred investing early, or if one's parents or aunts or uncles, etc., have done it for her or him, as in the above bucket illustration the magic of compounding results can be staggering.
$1000 in a tax-deferred account begun on a child's one-year birthday, left in place (or converted to other later fully invested tax-deferred accounts), and appreciating on average at 10% a year, becomes, by the time she or he is 61, $304,482, a greater than 3000% increase.
So, if one wants a child in the U.S. to eventually be a millionaire by the time she or he turns 62, when reduced Social Security benefits may begin, one might need "only" invest $3284 in a tax-deferred account in the child's name (by the 2nd birthday) in an asset or assets likely to appreciate 10% or better in the average year and convince the recipient, the only really hard part, to leave the account fully invested till retirement.