Compound interest doesn't just add up linearly—it multiplies exponentially. Each period's interest earns its own interest, creating a growth curve that bends sharply upward. Extend the time period and watch how fast the balance pulls away from the straight simple-interest line.
Simple interest calculates returns only on the original principal, giving you a straight line of growth. Compound interest recalculates each period on the new total, meaning your interest earns interest. Over 30 years at 5%, $10,000 becomes $25,000 with simple interest but $43,219 with compound. The gap widens exponentially: after 10 years simple gives $15,000, compound gives $16,289. After 20 years simple gives $20,000, compound gives $26,533. The longer you wait, the more powerful compounding becomes—which is why starting early matters far more than the amount you start with.
Final amount equals Principal times 1 plus rate raised to the number of periods—the exponent is what creates exponential growth, making interest earned on interest from previous periods far more valuable than simple interest alone.