Compound interest is often called the "eighth wonder of the world." Here's the actual math behind why it's so powerful.
Simple interest earns only on the original principal. $10,000 at 7% simple interest earns $700/year — always. After 30 years: $31,000 total.
Compound interest earns on both principal and accumulated interest. Year 1: $700 interest. Year 2: interest on $10,700 = $749. Year 3: interest on $11,449 = $801. After 30 years: $76,123 total — more than double the simple interest result.
Where: A = final amount, P = principal, r = annual rate (decimal), n = compounding periods/year, t = years. The magic is in the exponent — that's what creates exponential growth.
Compare two investors, both earning 7%/year. Investor A puts $5,000/year from age 25-35 (10 years, $50,000 total). Investor B puts $5,000/year from age 35-65 (30 years, $150,000 total). (Assuming contributions at the end of each year.) At 65, Investor A has roughly $526,000. Investor B has roughly $472,000 — despite contributing 3x more money. The 10 extra years of compounding for Investor A outweigh 20 more years of contributions for Investor B.
A 1% annual fee doesn't sound like much. On $10,000 at 7% over 30 years: no fee = $76,123. With 1% fee (6% net) = $57,435. The fee cost: $18,688 — nearly double the original investment. This is why low-cost index funds (0.03-0.2% fees) compound dramatically better than actively managed funds (0.5-1.5% fees) over long horizons.
Enter your starting amount, rate, and time horizon to see year-by-year growth.