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What is compound interest?
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00:00
When it comes to interest, it isn't always simple, but it doesn't need to be difficult to understand.
當談到利息時，它並不總是簡單的，但也無需難以理解。
00:05
Basically, interest usually falls into one of two groups, simple or compound.
基本上，利息通常分為兩種：單利或複利。
00:10
But what is the difference? And why did Albert Einstein reportedly call compound interest the eighth wonder of the world? Here's a quick crash course.
但兩者有何不同？為什麼據說阿爾伯特·愛因斯坦稱複利為世界第八大奇蹟？以下是一個快速入門課程。
00:18
First stop, what is interest? Let's take the example of savings accounts. Interest is the money paid to you by the bank as a reward for keeping your money with them. The interest is shown as a percentage per year, and is calculated based on the amount of money in your account. Simple interest
首先，什麼是利息？以儲蓄帳戶為例。利息是銀行支付給您的錢，作為您將錢存在他們那裡的獎勵。利息以每年的百分比表示，並根據您帳戶中的金額計算。單利
00:35
is just that, simple. The interest rate is applied to the amount in your account, principal only.
就是如此，很簡單。利率僅適用於您帳戶中的金額，也就是本金。
00:40
For example, if you have $1,000 earning 2% interest for a year, it would grow to $1,020 when the interest is paid at the end of the year. So the interest you receive over a certain period is a fixed percentage of the principal amount you deposited. How is compound interest different,
例如，如果您有 1,000 美元，賺取為期一年的 2% 利息，那麼在年底支付利息時，它將增長到 1,020 美元。因此，您在特定時期內收到的利息是您存入本金金額的固定百分比。複利有何不同，
00:58
you may ask? You could have heard it referred to as a magical interest, and there's a reason for that. Basically, you earn interest on the money you've deposited and also on the interest you've already earned. In other words, your interest earns interest. If you deposited the $1,000 into an account with a compound interest earning 2% per year compounded monthly, you would have $1,020
您可能會問？您可能聽過它被稱為神奇的利息，這是有原因的。基本上，您不僅能從存入的錢中賺取利息，還能從您已賺取的利息中賺取利息。換句話說，您的利息會再生利息。如果您將 1,000 美元存入一個年利率為 2%、按月複利的帳戶，一年後您將擁有 1,020 美元
01:20
and $0.18 at the end of the first year. This is because the interest is applied after the first month. Then the interest rate for month two is applied to the principal and interest and so on. So your money can grow at an accelerated rate over time. The impact is harder to see in
和 0.18 美元。這是因為利息是在第一個月後 applied（計算）。然後第二個月的利率會 applied 到本金和利息上，依此類推。因此，您的錢可以隨著時間以加速的方式增長。這種影響在
01:35
the early years, but eventually it becomes quite pronounced. Looking at our examples over a number of years can demonstrate the difference. Let's say you invested $1,000 every year into an account earning 5% simple interest each year and decided to withdraw the interest at the end of each year.
早期幾年較難看出，但最終會變得相當顯著。看看我們幾年來的示例可以證明這種差異。假設您每年投資 1,000 美元到一個每年賺取 5% 單利的帳戶，並決定在每年年底提取利息。
01:54
Over the 30 years, you would have saved $30,000 and earned $23,250 interest on top of that.
在 30 年期間，您將存下 30,000 美元，並在此基礎上賺取 23,250 美元的利息。
02:01
If you made the same investment with interest compounding monthly, with the same savings and 5% interest rate over the same 30 year period, your interest earned would increase to $41,247.57, with a total balance of $71,247.57. That's almost double the amount of interest earned when compared
如果您進行相同的投資，但利息按月複利，在相同的 30 年期間，使用相同的儲蓄和 5% 的利率，您賺取的利息將增加到 41,247.57 美元，總餘額為 71,247.57 美元。與我們的單利示例相比，這幾乎是所賺取利息金額的兩倍。
02:23
with our simple interest example. The extra interest is generated as a result of monthly compounding and leaving your interest in the account to earn additional interest over time.
額外的利息是由於每月複利以及將您的利息留在帳戶中隨時間賺取額外利息而產生的。
02:35
So the sooner you put your money into an account that is earning compound interest and leave it there, the faster your money will accumulate and the larger your savings will become.
因此，您越早將錢存入賺取複利的帳戶並留在那裡，您的錢累積得越快，您的儲蓄就會變得越多。
02:46
It's also worth remembering compound interest can work against you when you are the one paying it, such as with credit cards. So keep this in mind when considering your options.
同樣值得記住的是，當您是支付利息的一方時，例如使用信用卡時，複利也可能對您不利。因此，在考慮您的選擇時請記住這一點。
02:55
When it comes to compound interest, we tend to agree with Mr. Einstein, who also supposedly said that those who understand it, earn it, and those who don't, pay it. Which would you prefer to be in?
當談到複利時，我們傾向於同意愛因斯坦先生的觀點，據說他也曾說過，了解它的人會賺取它，而不了解的人則會支付它。您希望自己成為哪一種人？

What is compound interest?

📝 影片摘要

本單元深入解析複利（Compound Interest）的核心概念。課程從利息的基本定義出發，比較「單利」與「複利」的運作機制差異。透過 1,000 美元本金的實例，影片展示了複利如何透過「利滾利」的方式，讓資產在長期（如 30 年）內產生指數級的增長，其收益幾乎是單利模式的兩倍。此外，課程也提醒學習者，複利具有雙面性：當你是存款人時，它是累積財富的神奇工具；但當你是借款人（如使用信用卡）時，它可能成為沉重的負擔。最後引用愛因斯坦的名言，強調理解並善用複利的重要性。

📌 重點整理

  • ✓ 利息主要分為兩種：單利（Simple Interest）與複利（Compound Interest）。
  • ✓ 單利僅針對本金計算利息，公式固定且增長線性。
  • ✓ 複利被譽為世界第八大奇蹟，核心在於「利息也能賺取利息」（利滾利）。
  • ✓ 複利的效果在短期內不明顯，但隨時間拉長，資產增長速度會顯著加快。
  • ✓ 以 30 年投資為例，同樣 5% 年利率，複利收益幾乎是單利的兩倍。
  • ✓ 複利的頻率（如按月複利）會影響最終的總收益。
  • ✓ 當你借錢（如信用卡）時，複利會讓債務快速增加，對借款人不利。
  • ✓ 越早開始投資並利用複利，資產累積的效果越好。
📖 專有名詞百科 ｜點擊詞彙查看維基百科解釋
利息
interest
簡單的
simple
本金
principal
複利
compound
神奇的
magical
加速的
accelerated
顯著的
pronounced
提取
withdraw
餘額
balance
慷慨地
generously

🔍 自訂查詢

📚 共 10 個重點單字
interest /ˈɪntrəst/ noun
Money paid by a bank for keeping money in their account.
利息；作為將錢存入銀行的獎勵。
📝 例句
"Interest is the money paid to you by the bank as a reward for keeping your money with them."
→ 利息是銀行支付給您的錢，作為您將錢存在他們那裡的獎勵。
✨ 延伸例句
"The bank offers a high interest rate on savings."
→ 該銀行提供高利率的儲蓄方案。
simple /ˈsɪmpəl/ adjective
The interest rate is applied to the amount in your account, principal only.
簡單的；指單利的計算方式。
📝 例句
"Simple interest is just that, simple."
→ 單利就是如此，很簡單。
✨ 延伸例句
"The calculation for simple interest is straightforward."
→ 單利的計算非常直接。
principal /ˈprɪnsəpəl/ noun
The original amount of money deposited.
本金；最初存入的金額。
📝 例句
"The interest rate is applied to the amount in your account, principal only."
→ 利率僅適用於您帳戶中的金額，也就是本金。
✨ 延伸例句
"You will eventually get back your principal plus interest."
→ 你最終會拿回本金加上利息。
compound /ˈkɒmpaʊnd/ verb
To calculate interest on both the principal and the accumulated interest.
複利；將利息加入本金中再計算利息。
📝 例句
"How is compound interest different, you may ask?"
→ 複利有何不同，您可能會問？
✨ 延伸例句
"Money can compound quickly over time."
→ 金錢隨著時間能快速複利增長。
magical /ˈmædʒɪkəl/ adjective
Resembling magic; wonderful or extraordinary.
神奇的；像魔術般的。
📝 例句
"You could have heard it referred to as a magical interest."
→ 你可能聽過它被稱為神奇的利息。
✨ 延伸例句
"Compound interest seems magical in the long run."
→ 長期來看，複利似乎很神奇。
accelerated /əkˈseləreɪtɪd/ adjective
Happening at a faster rate.
加速的；速度加快的。
📝 例句
"So your money can grow at an accelerated rate over time."
→ 因此，您的錢可以隨著時間以加速的方式增長。
✨ 延伸例句
"Technology has led to accelerated growth in the industry."
→ 技術導致了該產業的加速成長。
pronounced /prəˈnaʊnst/ adjective
Very noticeable or marked.
顯著的；明顯的。
📝 例句
"The impact is harder to see in the early years, but eventually it becomes quite pronounced."
→ 這種影響在早期幾年較難看出，但最終會變得相當顯著。
✨ 延伸例句
"There is a pronounced difference between the two methods."
→ 這兩種方法之間存在顯著差異。
withdraw /wɪðˈdrɔː/ verb
To take money out of a bank account.
提取；取款。
📝 例句
"Decided to withdraw the interest at the end of each year."
→ 決定在每年年底提取利息。
✨ 延伸例句
"I need to withdraw some cash from the ATM."
→ 我需要從自動提款機提取一些現金。
balance /ˈbæləns/ noun
The amount of money in a bank account.
餘額；結餘。
📝 例句
"With a total balance of $71,247.57."
→ 總餘額為 71,247.57 美元。
✨ 延伸例句
"Please check your account balance regularly."
→ 請定期檢查你的帳戶餘額。
generously /ˈdʒenərəsli/ adverb
In a way that is more than adequate or expected.
慷慨地；豐富地。
📝 例句
"The extra interest is generated as a result of monthly compounding..."
→ 額外的利息是由於每月複利...
✨ 延伸例句
"The garden was generously planted with flowers."
→ 花園裡種滿了豐富的花卉。
🎯 共 10 題測驗

1 According to the video, what is the definition of interest in a savings account? 根據影片，儲蓄帳戶中的利息定義是什麼？ According to the video, what is the definition of interest in a savings account?

根據影片，儲蓄帳戶中的利息定義是什麼？

✅ 正確！ ❌ 錯誤，正確答案是 B

The video states: 'Interest is the money paid to you by the bank as a reward for keeping your money with them.'

影片指出：「利息是銀行支付給您的錢，作為您將錢存在他們那裡的獎勵。」

2 What characterizes 'Simple Interest' as described in the video? 如影片所述，「單利」的特徵是什麼？ What characterizes 'Simple Interest' as described in the video?

如影片所述，「單利」的特徵是什麼？

✅ 正確！ ❌ 錯誤，正確答案是 A

The video explains: 'The interest rate is applied to the amount in your account, principal only.'

影片解釋：「利率僅適用於您帳戶中的金額，也就是本金。」

3 If you deposit $1,000 at 2% simple interest for one year, what is the final amount? 如果你存入 1,000 美元，年利率 2% 單利一年，最終金額是多少？ If you deposit $1,000 at 2% simple interest for one year, what is the final amount?

如果你存入 1,000 美元，年利率 2% 單利一年，最終金額是多少？

✅ 正確！ ❌ 錯誤，正確答案是 B

The video gives an example: '...it would grow to $1,020 when the interest is paid at the end of the year.'

影片舉例：「...在年底支付利息時，它將增長到 1,020 美元。」

4 What is the core concept of compound interest? 複利的核心概念是什麼？ What is the core concept of compound interest?

複利的核心概念是什麼？

✅ 正確！ ❌ 錯誤，正確答案是 B

The video states: 'Basically, you earn interest on the money you've deposited and also on the interest you've already earned. In other words, your interest earns interest.'

影片指出：「基本上，您不僅能從存入的錢中賺取利息，還能從您已賺取的利息中賺取利息。換句話說，您的利息會再生利息。」

5 In the example of depositing $1,000 at 2% compounded monthly, what is the balance after one year? 在存入 1,000 美元、年利率 2% 按月複利的例子中，一年後的餘額是多少？ In the example of depositing $1,000 at 2% compounded monthly, what is the balance after one year?

在存入 1,000 美元、年利率 2% 按月複利的例子中，一年後的餘額是多少？

✅ 正確！ ❌ 錯誤，正確答案是 C

The video says: '...you would have $1,020 and $0.18 at the end of the first year.'

影片提到：「...一年後您將擁有 1,020 美元和 0.18 美元。」

6 Why does the balance grow to $1,020.18 instead of $1,020 in the monthly compounding example? 為什麼在按月複利的例子中，餘額會增長到 1,020.18 美元而不是 1,020 美元？ Why does the balance grow to $1,020.18 instead of $1,020 in the monthly compounding example?

為什麼在按月複利的例子中，餘額會增長到 1,020.18 美元而不是 1,020 美元？

✅ 正確！ ❌ 錯誤，正確答案是 B

The video explains: 'Then the interest rate for month two is applied to the principal and interest and so on.'

影片解釋：「然後第二個月的利率會 applied 到本金和利息上，依此類推。」

7 In the 30-year investment example, what is the total interest earned with simple interest (investing $1,000/year at 5%)? 在 30 年投資案例中，若使用單利（每年投資 1,000 美元，年利率 5%），總利息收入是多少？ In the 30-year investment example, what is the total interest earned with simple interest (investing $1,000/year at 5%)?

在 30 年投資案例中，若使用單利（每年投資 1,000 美元，年利率 5%），總利息收入是多少？

✅ 正確！ ❌ 錯誤，正確答案是 A

The video states: 'Over the 30 years, you would have saved $30,000 and earned $23,250 interest on top of that.'

影片指出：「在 30 年期間，您將存下 30,000 美元，並在此基礎上賺取 23,250 美元的利息。」

8 How much total interest is earned in the 30-year example with monthly compounding? 在 30 年案例中，若按月複利，總利息收入是多少？ How much total interest is earned in the 30-year example with monthly compounding?

在 30 年案例中，若按月複利，總利息收入是多少？

✅ 正確！ ❌ 錯誤，正確答案是 C

The video says: '...your interest earned would increase to $41,247.57...'

影片提到：「...您賺取的利息將增加到 41,247.57 美元...」

9 When can compound interest work against you? 複利在什麼情況下會對你不利？ When can compound interest work against you?

複利在什麼情況下會對你不利？

✅ 正確！ ❌ 錯誤，正確答案是 C

The video warns: 'It's also worth remembering compound interest can work against you when you are the one paying it, such as with credit cards.'

影片提醒：「同樣值得記住的是，當您是支付利息的一方時，例如使用信用卡時，複利也可能對您不利。」

10 According to the video, who earns compound interest and who pays it? 根據影片，誰賺取複利，誰支付複利？ According to the video, who earns compound interest and who pays it?

根據影片，誰賺取複利，誰支付複利？

✅ 正確！ ❌ 錯誤，正確答案是 A

The video concludes: '...those who understand it, earn it, and those who don't, pay it.'

影片結論：「了解它的人會賺取它，而不了解的人則會支付它。」

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