Definition and Difference from Simple Interest
Compound interest is the mechanism by which interest accrues not only on the original principal but also on previously earned interest. While simple interest calculates returns on the principal alone, compound interest produces snowball-like growth. Investing one million yen at 5% annual interest yields two million after 20 years under simple interest, but roughly 2.65 million under compound interest. The gap widens dramatically over longer time horizons.
The Rule of 72
The Rule of 72 is a quick method for estimating how long it takes an investment to double. Divide 72 by the annual interest rate to get the approximate number of years. At 6% per year, assets double in about 12 years; at 3%, in about 24 years.
This rule applies equally to inflation. If prices rise at 3% annually, they double in 24 years, effectively halving purchasing power. The force of compounding works both for and against you depending on which side of the equation you are on.
Wealth Inequality and r > g
Thomas Piketty's inequality "r > g" - where the return on capital exceeds the economic growth rate - captures how compounding widens wealth gaps over time. Those who hold capital grow their assets through compound returns, while those relying solely on labor income fall further behind. The concentration of wealth at the top of global asset rankings is, in large part, the long-run consequence of compound interest.
Connection to Financial Literacy
Understanding compound interest is the cornerstone of financial literacy. When you check your position on an income or asset ranking, what matters more than your current rank is how compounding will shape your trajectory going forward. The gap between someone who started investing early and someone who started late is explained less by ability or income and more by the duration over which compounding has operated. A ranking is a snapshot of the present; compound interest determines the future path.