The Difference Between Simple and Compound Interest — Interest on Interest
Did you know interest comes in different types? Simple interest is added only to the principal, while compound interest adds interest on top of interest. This small difference becomes an enormous gap 30 years later.
Simple vs. Compound: The Difference in Calculation
Simple interest is added 'only to the principal.' The formula is simple: interest = principal × rate × time. If you put about $740 at 5% simple interest for 3 years, about $37 in interest is added each year, totaling about $111 over three years, so it becomes about $851. The interest is the same every year.
Compound interest is added to 'the principal plus the interest accumulated so far.' Future value = principal × (1 + rate)^time. With the same about $740 at 5% compound interest for 3 years, year one adds about $37, year two adds 5% of about $777 (about $38.9), and year three adds 5% of about $816 (about $40.8), so it becomes about $857.
Even over just 3 years, compound interest yields about $5.6 more than simple interest. As both the amount and the time grow, this gap snowballs.
Simple interest grows in a 'steady straight line,' while compound interest grows in a 'curve that gets steeper and steeper.' Over a short horizon the difference looks small, but over a longer one the curve far outpaces the line.
The Gap That Widens with Time, and a Famous Misconception
The power of compounding comes from 'time.' Early on it looks barely different from simple interest, but after 20 or 30 years the compound curve shoots up sharply. That's why people say 'starting early' is as important as 'putting in a lot.'
A well-known saying goes, 'Compound interest is the eighth wonder of the world; he who understands it earns it, he who doesn't pays it,' often attributed to Einstein as a famous quote. However, according to various fact-checks, no reliable basis has been confirmed that Einstein actually said this. Some analyses suggest it originated in bank advertising copy of the 1920s–30s. Even if the quote's origin is uncertain, the power of compounding itself is a mathematically clear fact.
The 'Einstein said it' part is a misattribution (a quote falsely pinned on someone) with no confirmed basis. But the principle that compounding grows explosively over time is true.
常见问题
Q. How can I enjoy compounding?
The key is 'reinvesting your interest, dividends, and gains.' If you withdraw interest and spend it, it becomes closer to simple interest; if you fold it back into the principal, compounding rolls forward. Reinvesting dividends, or continuing to grow your gains without withdrawing them, is how you realize compounding.
Q. Does the result change depending on the compounding frequency (yearly, monthly, daily)?
Yes. Even at the same annual rate, the more frequently interest is added (monthly, daily compounding), the slightly larger the final amount. The 'true annual rate' that reflects this difference is the effective annual rate (EAR). That said, the difference from frequency is not as large as the difference from time or rate.
📋 结果基于历史数据计算,过去的收益不代表未来的收益。
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