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Simple vs. Compound Interest
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00:05
Hello and welcome, today we will be discussing compound interest.
大家好，歡迎收看，今天我們將討論複利。
00:11
Compound interest is interest that is paid not only on the initial principle of a loaner, deposit but also on the accumulated interest from previous periods of the loaner deposit.
複利是指不僅針對貸款或存款的初始本金計算利息，還會將先前期間累積的利息一併計算。
00:21
Basically, compound interest can be thought of as interest on interest.
基本上，複利可以被視為利息的利息。
00:26
In order to properly understand how compound interest works, we must first understand what simple interest is.
為了正確理解複利的運作方式，我們必須先了解什麼是單利。
00:34
Simple interest is interest that is paid only on the initial principle of a loaner deposit and not on any interest that is earned during the term of the loaner deposit.
單利是指僅針對貸款或存款的初始本金計算利息，而不針對貸款或存款期間內賺取的任何利息計算。
00:44
Basically, simple interest is interest on principle and nothing else.
基本上，單利就是針對本金計算的利息，沒有其他項目。
00:49
In order to differentiate between simple and compound interest, consider the example of Daniel and Claire.
為了區分單利和複利，我們來看看 Daniel 和 Claire 的例子。
00:57
Daniel and Claire each deposit $10,000 in high interest savings accounts.
Daniel 和 Claire 各自將 10,000 美元存入高利率儲蓄帳戶。
01:02
However, the bank that Daniel has deposited his money at offers only simple interest while the bank that Claire has deposited her money at offers compound interest.
然而，Daniel 存款的銀行只提供單利，而 Claire 存款的銀行則提供複利。
01:13
After the first year, both Daniel and Claire made $500, or 5% on their initial deposit.
第一年後，Daniel 和 Claire 都賺了 500 美元，也就是他們初始存款的 5%。
01:20
However, for all subsequent years their return on investment, or ROI, will be different.
然而，在接下來的所有年份中，他們的投資報酬率（ROI）將會不同。
01:26
Because Daniel's bank only offers simple interest, he will continue to make $500, or 5% of his principal investment of $10,000 each year.
因為 Daniel 的銀行只提供單利，他將繼續每年賺取 500 美元，也就是他 10,000 美元本金投資的 5%。
01:36
On the other hand, because Claire's bank offers compound interest, she will make 5% on not only her principal investment of $10,000 but also on her accumulated interest from previous periods.
另一方面，因為 Claire 的銀行提供複利，她將針對 10,000 美元的本金以及先前期間累積的利息賺取 5% 的報酬。
01:50
So in year two, Claire will earn 5% on both her principal as well as on the interest that she earned in year one, rather than 5% on only her principal deposit of $10,000.
所以在第二年，Claire 將針對本金以及她在第一年賺取的利息賺取 5%，而不僅僅是針對她 10,000 美元的本金存款賺取 5%。
02:01
With this in mind, Claire will earn $525 in year two, bringing her total capital to $11,025.
考量到這點，Claire 在第二年將賺取 525 美元，使她的總資本達到 11,025 美元。
02:11
Meanwhile, Daniel will earn only $500 in year two, bringing his total capital to $11,000.
同時，Daniel 在第二年僅賺取 500 美元，使他的總資本達到 11,000 美元。
02:18
So, after year two, Claire has made $25 more than Daniel, all without lifting a finger.
因此，在第二年結束後，Claire 比 Daniel 多賺了 25 美元，而她完全不費吹灰之力。
02:25
In year three, Daniel will once again make $500, or 5% of his principal investment of $10,000 with simple interest, bringing his total capital to $11,500.
在第三年，Daniel 將再次賺取 500 美元，也就是他 10,000 美元本金以單利計算的 5%，使他的總資本達到 11,500 美元。
02:38
Claire, on the other hand, will make 5% of $11,025 in year three, for an annual return of $551.25, bringing her total capital to $11,576.25.
另一方面，Claire 在第三年將賺取 11,025 美元的 5%，年報酬為 551.25 美元，使她的總資本達到 11,576.25 美元。
02:54
So, after only two years, Claire has made $76.25 more than Daniel, all due to compound interest.
因此，僅僅兩年後，Claire 就比 Daniel 多賺了 76.25 美元，這完全歸功於複利。
03:03
While this may seem like an inconsequential amount of money, it is important to remember that the effects of compound interest increase over time.
雖然這看起來可能是一筆微不足道的金額，但重要的是要記住，複利的效應會隨時間增加。
03:11
As we can see from this example, Claire's annual return on investment increased by $26.25, all the way from $525 to $551.25, just from year two to year three.
從這個例子可以看出，克萊爾的年投資報酬率從 525 美元增加到 551.25 美元，僅在第二年到第三年之間就增加了 26.25 美元。
03:27
And the effects of compound interest are even more profound when we compare Daniel and Claire's return on investment over a 10-year horizon.
當我們比較丹尼爾和克萊爾在 10 年期間的投資報酬率時，複利的效應更加顯著。
03:34
With Claire's annual return climbing from $500 all the way to approximately $775.
克萊爾的年回報從 500 美元一路攀升至約 775 美元。
03:43
In summary, simple interest is interest that is paid only on the initial principal of a loan or deposit.
總結來說，單利是指僅對貸款或存款的初始本金支付利息。
03:50
On the other hand, compound interest is interest that is paid on both the principal of a loan or deposit, as well as on the interest that is accumulated from the loan or deposit.
另一方面，複利是指對貸款或存款的本金，以及從該筆貸款或存款累積的利息支付利息。
04:00
While in the short term, the difference in returns between simple and compound rates of interest is negligible.
雖然在短期內，單利和複利之間的回報差異微乎其微。
04:07
Over the longer term, compound interest offers markedly better returns.
但從長期來看，複利能提供顯著更好的回報。
04:11
Thanks for watching, and as always, if you have any further questions, please do not hesitate to give us a call or visit our website.
感謝您的觀看，一如既往，如果您有任何進一步的問題，請隨時致電或造訪我們的網站。

Simple vs. Compound Interest

📝 影片摘要

本單元深入剖析單利（Simple Interest）與複利（Compound Interest）的差異。透過丹尼爾（Daniel）與克萊爾（Claire）的投資案例比較，影片展示了兩種計息方式在短期與長期的顯著不同。單利僅針對初始本金計算利息，而複利則是將本金與前期累積的利息一同計息，也就是「利滾利」。雖然在第一年兩者的回報相同，但隨著時間拉長，複利能產生指數級的增長，提供遠超單利的投資報酬。

📌 重點整理

  • ✓ 複利的定義：利息不僅基於本金，還基於前期累積的利息。
  • ✓ 單利的定義：利息僅基於初始本金計算。
  • ✓ 兩者第一年的回報相同，均為本金的 5%。
  • ✓ 第二年，克萊爾（複利）獲得 $525，丹尼爾（單利）獲得 $500。
  • ✓ 第三年，克萊爾的年回報增至 $551.25，顯示出加速增長。
  • ✓ 長期來看，複利與單利的差距會隨時間急劇擴大。
  • ✓ 十年後，克萊爾的年回報將從 $500 攀升至約 $775。
  • ✓ 結論：短期內差異微小，但長期持有下複利能提供顯著更好的回報。
📖 專有名詞百科 ｜點擊詞彙查看維基百科解釋
複利
compound interest
單利
simple interest
本金
principal
存款
deposit
投資回報率
return on investment
累積的
accumulated
隨後的
subsequent
微不足道的
negligible
視野
horizon
深遠的
profound

🔍 自訂查詢

📚 共 10 個重點單字
compound interest /kəmˈpaʊnd ˈɪntrəst/ noun
interest calculated on the initial principal and also on the accumulated interest of previous periods.
複利；複利是指對貸款或存款的本金，以及從該筆貸款或存款累積的利息支付利息。
📝 例句
"Compound interest is interest that is paid not only on the initial principle of a loaner, deposit but also on the accumulated interest from previous periods of the loaner deposit."
→ 複利是指利息不僅支付給借款者或存款的初始本金，還支付給該筆借款或存款在先前期間累積的利息。
✨ 延伸例句
"Basically, compound interest can be thought of as interest on interest."
→ 基本上，複利可以被視為利息上的利息。
simple interest /ˈsɪmpəl ˈɪntrəst/ noun
interest calculated solely on the principal amount of a loan or deposit.
單利；僅對貸款或存款的初始本金支付利息。
📝 例句
"Simple interest is interest that is paid only on the initial principle of a loaner deposit and not on any interest that is earned during the term of the loaner deposit."
→ 單利是指僅對借款者或存款的初始本金支付利息，而不對借款或存款期間賺取的任何利息支付利息。
✨ 延伸例句
"Basically, simple interest is interest on principle and nothing else."
→ 基本上，單利是基於本金的利息，不包含其他部分。
principal /ˈprɪnsəpəl/ noun
the original sum of money borrowed in a loan or put into an investment.
本金；投資或借款的原始金額。
📝 例句
"Simple interest is interest that is paid only on the initial principle of a loaner deposit..."
→ 單利是指僅對借款者或存款的初始本金支付利息...
✨ 延伸例句
"He will continue to make $500, or 5% of his principal investment of $10,000 each year."
→ 他每年將繼續賺取 500 美元，也就是他 10,000 美元本金投資的 5%。
deposit /dɪˈpɒzɪt/ noun
a sum of money placed in a bank account.
存款；存入銀行帳戶的金額。
📝 例句
"Daniel and Claire each deposit $10,000 in high interest savings accounts."
→ 丹尼爾和克萊爾各自存了 10,000 美元到高利率儲蓄帳戶中。
✨ 延伸例句
"The bank requires a minimum deposit of $500."
→ 銀行要求最低存款 500 美元。
return on investment /rɪˈtɜːn ɒn ɪnˈvestmənt/ noun
the gain or loss generated on an investment relative to the amount of money invested.
投資回報率（ROI）；相對於投資金額所產生的收益或損失。
📝 例句
"However, for all subsequent years their return on investment, or ROI, will be different."
→ 然而，在接下來的所有年份中，他們的投資回報率（ROI）將會不同。
✨ 延伸例句
"Claire's annual return on investment increased by $26.25."
→ 克萊爾的年投資回報率增加了 26.25 美元。
accumulated /əˈkjuːmjʊleɪtɪd/ adjective
gathered or acquired over a period of time.
累積的；一段時間內收集或獲得的。
📝 例句
"Because Claire's bank offers compound interest, she will make 5% on not only her principal investment of $10,000 but also on her accumulated interest from previous periods."
→ 因為克萊爾的銀行提供複利，她不僅能從 10,000 美元的本金投資中賺取 5%，還能從先前期間累積的利息中賺取 5%。
✨ 延伸例句
"The accumulated interest makes a big difference over time."
→ 累積的利息隨著時間的推移會產生巨大的差異。
subsequent /ˈsʌbsɪkwənt/ adjective
occurring or coming later or after something.
隨後的；繼某事之後發生的。
📝 例句
"However, for all subsequent years their return on investment, or ROI, will be different."
→ 然而，在接下來的所有年份中，他們的投資回報率（ROI）將會不同。
✨ 延伸例句
"The first year was the same, but subsequent years showed a difference."
→ 第一年是一樣的，但隨後的年份顯示出差異。
negligible /ˈneɡlɪdʒəbəl/ adjective
so small or unimportant as to be not worth considering.
微不足道的；極小或不重要而不值得考慮的。
📝 例句
"While in the short term, the difference in returns between simple and compound rates of interest is negligible."
→ 雖然在短期內，單利和複利之間的回報差異微乎其微。
✨ 延伸例句
"The cost difference between the two options is negligible."
→ 這兩個選項之間的成本差異微不足道。
horizon /həˈraɪzən/ noun
the limit of a person's knowledge, experience, or interest; often used to describe a time frame.
視野；地平線。在財經中常指時間範圍或投資期限。
📝 例句
"And the effects of compound interest are even more profound when we compare Daniel and Claire's return on investment over a 10-year horizon."
→ 當我們比較丹尼爾和克萊爾在 10 年期間的投資回報時，複利的效應更加顯著。
✨ 延伸例句
"Investors should plan for a long-term horizon."
→ 投資者應該為長期規劃做準備。
profound /prəˈfaʊnd/ adjective
having a very great depth or intensity.
深遠的；極度的或強烈的。
📝 例句
"And the effects of compound interest are even more profound when we compare Daniel and Claire's return on investment over a 10-year horizon."
→ 當我們比較丹尼爾和克萊爾在 10 年期間的投資回報時，複利的效應更加顯著。
✨ 延伸例句
"The changes had a profound effect on the company."
→ 這些變動對公司產生了深遠的影響。
🎯 共 10 題測驗

1 What is the definition of compound interest according to the video? 根據影片，什麼是複利？ What is the definition of compound interest according to the video?

根據影片，什麼是複利？

✅ 正確！ ❌ 錯誤，正確答案是 B

The video states that compound interest is paid on both the principal and the accumulated interest from previous periods.

影片指出，複利是基於本金以及先前期間累積的利息來支付的。

2 How much did Daniel and Claire each deposit initially? 丹尼爾和克萊爾最初各存了多少錢？ How much did Daniel and Claire each deposit initially?

丹尼爾和克萊爾最初各存了多少錢？

✅ 正確！ ❌ 錯誤，正確答案是 C

At [57], the video mentions they each deposit $10,000.

在 [57] 秒，影片提到他們各自存了 10,000 美元。

3 What was the annual interest rate used in the example? 範例中使用的年利率是多少？ What was the annual interest rate used in the example?

範例中使用的年利率是多少？

✅ 正確！ ❌ 錯誤，正確答案是 B

At [73], it is stated that both made $500, which is 5% on their $10,000 deposit.

在 [73] 秒，提到兩人都賺了 500 美元，這是他們 10,000 美元存款的 5%。

4 Which account offers simple interest? 哪個帳戶提供單利？ Which account offers simple interest?

哪個帳戶提供單利？

✅ 正確！ ❌ 錯誤，正確答案是 B

The video explicitly states that Daniel's bank offers only simple interest.

影片明確指出丹尼爾的銀行只提供單利。

5 How much interest did Claire earn in the second year? 克萊爾在第二年賺了多少利息？ How much interest did Claire earn in the second year?

克萊爾在第二年賺了多少利息？

✅ 正確！ ❌ 錯誤，正確答案是 B

At [121], the video states Claire earned $525 in year two.

在 [121] 秒，影片指出克萊爾在第二年賺了 525 美元。

6 What is the total capital Claire has after year two? 克萊爾在第二年後的總資本是多少？ What is the total capital Claire has after year two?

克萊爾在第二年後的總資本是多少？

✅ 正確！ ❌ 錯誤，正確答案是 B

At [121], the text says her total capital is $11,025.

在 [121] 秒，字幕顯示她的總資本為 11,025 美元。

7 By how much did Claire's annual return increase from year two to year three? 從第二年到第三年，克萊爾的年回報增加了多少？ By how much did Claire's annual return increase from year two to year three?

從第二年到第三年，克萊爾的年回報增加了多少？

✅ 正確！ ❌ 錯誤，正確答案是 B

At [191], the video mentions an increase of $26.25, from $525 to $551.25.

在 [191] 秒，影片提到增加了 26.25 美元，從 525 美元增加到 551.25 美元。

8 What is Daniel's total capital after three years? 丹尼爾三年後的總資本是多少？ What is Daniel's total capital after three years?

丹尼爾三年後的總資本是多少？

✅ 正確！ ❌ 錯誤，正確答案是 A

At [145], it states Daniel's total capital is $11,500 after year three.

在 [145] 秒，指出丹尼爾三年後的總資本為 11,500 美元。

9 Over what time horizon does the difference between simple and compound interest become more profound? 在什麼時間範圍內，單利和複利之間的差異變得更加顯著？ Over what time horizon does the difference between simple and compound interest become more profound?

在什麼時間範圍內，單利和複利之間的差異變得更加顯著？

✅ 正確！ ❌ 錯誤，正確答案是 D

At [207], the video discusses the profound effects of compound interest over a 10-year horizon.

在 [207] 秒，影片討論了在 10 年期間複利的深遠效應。

10 What is the main conclusion of the video regarding compound interest? 影片關於複利的主要結論是什麼？ What is the main conclusion of the video regarding compound interest?

影片關於複利的主要結論是什麼？

✅ 正確！ ❌ 錯誤，正確答案是 B

At [247], the video concludes that over the longer term, compound interest offers markedly better returns.

在 [247] 秒，影片總結道，長期來看，複利能提供顯著更好的回報。

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