Compound interest is what happens when the returns on money are reinvested and start producing returns of their own. Simple interest on $10,000 at 7% is $700 every year forever. Compound interest pays $700 the first year, then 7% of $10,700 the second year, then 7% of $11,449, and so on. The difference is small at first and enormous later.
After 10 years at 7%, $10,000 becomes about $19,700. After 20 years, $38,700. After 30 years, $76,100. After 40, $149,700. The first decade added under $10,000; the fourth added over $73,000. Nothing changed except time.
A quick shortcut is the rule of 72: divide 72 by the annual return to get the number of years to double. At 7%, money doubles roughly every 10 years. At 10%, every 7 years. At 3%, every 24.
The same mechanism works against you with debt. A credit card at 24% doubles an unpaid balance in about three years, which is why paying it off is one of the highest-return moves available.
The common mistake is waiting for a bigger income before starting. $300 a month from age 25 at 7% grows to about $790,000 by 65. Starting at 35, it reaches about $370,000. The ten-year delay costs more than $400,000, far more than the $36,000 that was not contributed. Time is the ingredient that cannot be bought back.