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.

Balance on one million yen at 5% annual interest under simple versus compound interest
Years elapsedSimple interestCompound interestDifference
5 years1.250 million yen1.276 million yen26,000 yen
10 years1.500 million yen1.629 million yen129,000 yen
20 years2.000 million yen2.653 million yen653,000 yen
30 years2.500 million yen4.322 million yen1,822,000 yen
40 years3.000 million yen7.040 million yen4,040,000 yen
Balances assume a principal of one million yen, a 5% annual return, and no deposits or withdrawals along the way. Simple interest adds a flat 50,000 yen every year, so it grows in a straight line; compound interest also earns 5% on the interest already added, opening a gap of 129,000 yen by year 10 and 4,040,000 yen by year 40. The "roughly 2.65 million after 20 years" figure above is the 20-year row. Notice how little separates the two columns early on - that is precisely why compounding is so easy to underestimate.

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.

Doubling time estimated by the Rule of 72 compared with the exact compound calculation
Annual rateRule of 72 estimateExact doubling time
2%36 years35.0 years
3%24 years23.4 years
4%18 years17.7 years
6%12 years11.9 years
8%9 years9.0 years
12%6 years6.1 years
The right-hand column is the exact compound doubling time. The Rule of 72 is nearly perfect around 8%, runs slightly long at lower rates and slightly short at higher ones, yet never misses by more than a single year across this range. The 3% row, for instance, estimates 24 years against an exact 23.4 - and that same 24-year figure holds whether the 3% is an investment return or an inflation rate.

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.