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Simple interest pays only on your original principal every year, so growth is linear: $10,000 at 6% earns $600 every year, forever. Compound interest pays on principal plus all previously earned interest, so growth is exponential. At 6% compounded monthly, the same $10,000 reaches about $18,194 after 10 years (compound) versus $16,000 (simple). Over 30 years the gap widens dramatically: roughly $60,225 versus $28,000. The longer your time horizon, the more compound pulls away.

Yes, but with sharply diminishing returns. At a 6% nominal rate over 10 years on $10,000, annual compounding gives $17,908, monthly gives $18,194, and daily gives $18,221. Daily compounds about 0.15% more than monthly, and continuous compounding barely beats daily. Most US high-yield savings and money-market accounts compound daily, CDs are typically daily or monthly, and bonds usually compound semi-annually. The frequency a bank advertises matters less than the effective annual rate (also called APY).

The Rule of 72 is a mental-math shortcut: divide 72 by your annual return percent to estimate the years it takes your money to double. At 6%, money doubles in about 12 years. At 8%, about 9 years. At 12%, about 6 years. The approximation is accurate to within about 1% for rates between 6% and 10% and is the best back-of-the-envelope test for any compound-growth claim. It does not apply at zero or negative rates because nothing doubles.

Almost certainly not. The quote is apocryphal, with no documented source in Einstein's letters, papers, or interviews. The earliest known appearances are from advertising and personal-finance writing decades after his death. The line stuck because the underlying point is sound: exponential growth over long horizons produces results that feel almost magical. Whoever first said it, the math is what matters, not the attribution.

Both, depending on which side of the loan you are on. In a savings account, retirement plan, or long-term investment, compounding works for you: every dollar of interest joins the principal and starts earning its own interest. In credit-card debt, payday loans, or any revolving balance, the same math runs against you: unpaid interest is added to the balance and starts accruing more interest, which is why a 24% APR card can double a balance in roughly three years if you only pay the minimum. The lesson is to be on the savings side as early and as often as possible, and to get off the debt side as fast as possible.