Compound interest is interest earning interest. Each period's gains join your balance and start earning their own return — which is why the growth curve bends upward instead of climbing in a straight line. The three levers are your starting amount, your regular contributions, and the rate, but the quiet fourth lever is time: most of the growth happens late, so starting early matters more than almost anything else.
Start with $10,000, add $200/mo, and assume a 7% annual return compounded monthly. After 20 years you'd have about $144,600.
You only contributed $58,000 of that — the other ~$86,600 is interest. Push the time horizon to 30 years and the interest portion grows dramatically faster than the contributions, because the earliest dollars have had the longest to compound.
A mental shortcut: divide 72 by your rate to estimate years to double your money. At 7%, that's about 10.3 years — very close to the exact 10.2, which is why the rule has stuck around.
A little. Daily vs. annual compounding at the same rate makes a modest difference over long horizons — real and worth knowing, but far smaller than changing the rate, contribution, or time.
Nominal is the headline rate; real is what's left after inflation erodes purchasing power. A 7% nominal return at 3% inflation is closer to a 4% real return — the number that reflects what you can actually buy later.
No — real investments vary year to year, sometimes sharply. This model assumes a steady average, which is useful for intuition but will never match any actual sequence of returns.