In the last video, we learned all about the different financial institutions and the services they provide.

在上一段視頻中，我們瞭解了不同的金融機構及其提供的服務。

But one big question was left unanswered.

但有一個大問題沒有得到解答。

What is interest?

什麼是利息？

And why is it such a big deal for savings accounts and loans?

為什麼對儲蓄賬戶和貸款如此重要？

Well, in this lesson, you're gonna learn the answers to those burning questions.

那麼，在本課中，你將瞭解到這些迫切問題的答案。

By the end of this lesson, you'll be able to compare interest rates, identify preferable rates and calculate accrued interest.

在本課結束時，您將能夠比較利率、識別優惠利率並計算應計利息。

To achieve that objective, we're gonna first discuss the basis of what interest is.

為了實現這一目標，我們首先要討論什麼是興趣的基礎。

Then we'll look at how the two main types of interest, simple interest and compound interest work and how they're calculated.

然後，我們來看看單利和複利這兩種主要利息是如何運作和計算的。

We'll also learn about the rule of 72, a valuable tool for estimating how quickly compound interest grows.

我們還將學習 72法則，這是估算複利增長速度的重要工具。

Let's get into it.

讓我們開始吧。

In finances, when we say interest, we're referring to an extra charge paid for the privilege of borrowing money.

在金融學中，當我們說到利息時，我們指的是為借錢而支付的額外費用。

Essentially, interest is what you pay to get a loan.

從根本上說，利息就是為獲得貸款而支付的費用。

Imagine Marco's got plenty of money, but Jimmy over here is flat broke.

想象一下，馬可有很多錢，而這邊的吉米卻身無分文。

Jimmy needs some cash bad, so he asks Marco for some money.

吉米急需現金，於是向馬可借錢。

Marco agrees to loan Jimmy the money, but is going to charge him interest.

馬可同意借錢給吉米，但要收取利息。

Jimmy will pay back Marco in small amounts until he's paid back all the money he borrowed plus a little extra as thanks for letting him borrow the money.

吉米會分期分批還錢給馬可，直到他還清所有借的錢，外加一點額外的錢，以感謝他借錢給他。

That extra amount is the interest.

這筆額外的金額就是利息。

When it comes to interest, there are two main types.

說到利息，主要有兩種類型。

The first type is simple interest.

第一種是單利。

With simple interest, you pay interest only on what you borrowed initially.

單利計算時，您只需支付最初借款的利息。

This amount is called the principal, and your goal is to pay that off.

這筆金額被稱為本金，您的目標是還清本金。

Simple interest is most commonly used for auto loans and personal loans.

單利最常用於汽車貸款和個人貸款。

How simple interest works isn't the only thing that makes it simple.

單利的運作方式並不是使它變得簡單的唯一原因。

The formula for calculating it is pretty simple too.

計算公式也很簡單。

To calculate how much interest accrues, you only need to multiply three things together.

要計算應計利息，只需將三項相乘即可。

The principal amount, the annual interest rate, and how many years you'll take to pay it off.

本金數額、年利率以及您需要多少年才能還清。

To make the equation a little more condensed, we can remove the multiplication dots since it's assumed to be multiplication anyway.

為了使等式更簡潔，我們可以去掉乘法點，因為無論如何，我們都假定它是乘法。

Add the principal to that, and you get the total amount that will be owed.

再加上本金，就是欠款總額。

Although, usually, you'll see it written in this form, which factors out the P from both terms so that you only have to plug in the principal once.

不過，你通常會看到這種寫法，它將兩個條件中的 P 都係數化了，這樣你只需輸入一次本金。

Let's check out some examples of that.

讓我們來看看這方面的一些例子。

Let's say you borrow $1,000 from me.

假設你向我借了 1000 美元。

If you need to, just let me know.

如果需要，請告訴我。

I'll charge you 4% annual interest and give you two years to pay me back.

我會向你收取 4% 的年利率，並給你兩年時間還錢。

To figure out how much you'll owe me, we can use the total amount formula.

要計算出你欠我多少錢，我們可以使用總額公式。

Replace the variables with their corresponding values, and evaluate.

將變量替換為相應的值，然後求值。

The total amount you'll owe me is $1,080.

你欠我的總金額為 1,080 美元。

You can afford that, right?

你負擔得起，對嗎？

This is just a basic example of simple interest, but we'll discuss it more in depth in the unit on loans.

這只是單利的一個基本例子，我們將在 "貸款 "單元中進行更深入的討論。

In the last video, we mentioned savings and checking accounts, which utilize compound interest instead.

在上一段視頻中，我們提到了儲蓄和支票賬戶，它們利用的是複利。

Compound interest is, well, it's not simple.

複利並不簡單。

See, compound interest accrues interest not just on the principal, but also on the interest that has already accrued.

你看，複利不僅對本金產生利息，還對已經產生的利息產生利息。

In other words, you pay interest on the interest.

換句話說，你要為利息支付利息。

The more interest you allow to accrue, the more interest will accrue the next time, and the next time, and the next.

你允許累積的利息越多，下一次、下下一次、下下下一次累積的利息就越多。

This is known as compounding, and compounding can happen on any schedule, yearly, monthly, even daily.

這就是所謂的複利，複利可以按任何時間表進行，每年、每月甚至每天。

It can get really out of hand really quickly, which is why it's good to have compounding interest on a savings account, and not so great to have it on a student loan.

這種情況很快就會失控，這就是為什麼儲蓄賬戶有複利是好事，而學生貸款就沒那麼好了。

Whereas the formula for simple interest is simple, the formula for compound interest is anything but simple.

單利的計算公式很簡單，而複利的計算公式卻不簡單。

When we say compound interest grows exponentially, we mean it.

當我們說複利呈指數增長時，我們是認真的。

There's an exponent right there in the formula, and that exponent is why compound interest grows faster and faster.

公式中有一個指數，這個指數就是複利增長越來越快的原因。

But let's take it one step at a time, because there are a lot of variables in this formula.

但我們還是要一步一步來，因為這個公式中有很多變量。

The first variable you should already recognize.

第一個變量你應該已經認識到了。

It's the principal, or the amount that you initially borrowed.

這是本金，即您最初借貸的金額。

R should look familiar too.

R 應該也很眼熟。

Just like before, it's the yearly interest rate.

和以前一樣，這是年利率。

Oh, and T is once again the amount of years.

哦，T 又是年數。

Okay, so most of the variables are the same.

好吧，大部分變量都是一樣的。

What about this N that appears twice?

這個出現兩次的 N 又是怎麼回事？

That's a major part of compound interest.

這是複利的主要部分。

It's how often the interest is compounded each year.

這是每年複利計算的頻率。

By putting all of this together, we can calculate the total amount owed on the loan.

將所有這些加在一起，我們就可以計算出貸款欠款總額。

If we wanted to know only how much interest is accrued, we would then just subtract the principal from the total.

如果我們只想知道應計利息，那麼只需從總數中減去本金即可。

Let's do a quick example.

讓我們舉個簡單的例子。

Let's say that, after you borrowed those $1,000 from me before, you realized you didn't wanna have to do that again.

比方說，你之前向我借了 1000 美元后，意識到不想再借了。

So you deposit $1,000 into a savings account.

於是，你將 1000 美元存入儲蓄賬戶。

Remember, when you deposit money into a savings account, you're actually loaning your money to the financial institution, which means they're gonna owe you interest.

記住，當你把錢存入儲蓄賬戶時，你實際上是把錢借給了金融機構，這意味著他們會欠你利息。

Oddly enough, your savings account has the same interest rate that I gave you, 4%.

奇怪的是，你的儲蓄賬戶利率和我給你的一樣，都是 4%。

You deposit this money, and then leave it alone for two whole years.

你存入這筆錢，然後整整兩年都不用管它。

Basically, the terms of loaning your money to the bank is exactly the same as my loan to you, except it compounds quarterly, meaning four times a year.

基本上，把你的錢借給銀行的條件和我借給你的條件是完全一樣的，只不過是每季度複利一次，也就是一年四次。

With this information, do you think you'd be able to calculate the total amount?

有了這些資訊，你認為你能計算出總額嗎？

Remember, since this is compound interest, we need the formula for the total amount from compound interest, not simple interest.

請記住，由於這是複利，我們需要的是複利總額的計算公式，而不是單利的計算公式。

Pause the video here and see if you can calculate how much you'll end up with.

在此暫停視頻，看看能否計算出最終會有多少錢。

When we plug in all of our variables, this is what we get.

當我們把所有變量都輸入後，得到的結果是這樣的。

The easiest way to evaluate it is to type it into a calculator, just like this.

最簡單的評估方法是將其輸入計算器，就像這樣。

That symbol before the exponent is called a caret, and the button usually looks something like this.

指數前的符號稱為 "刻度線"，按鈕通常看起來像這樣。

You can use it anytime you need to type an exponent into your calculator.

需要在計算器中輸入指數時，隨時都可以使用它。

Once we type it in, we just hit Enter, and we get this answer.

輸入後，按下回車鍵，就能得到這個答案。

We started with $1,000 and gained $82.86 in interest.

我們從 1,000 美元開始，獲得了 82.86 美元的利息。

But what happened in between?

但這中間發生了什麼？

To understand that, we have to understand the pieces of the formula.

要理解這一點，我們必須瞭解公式的各個部分。

This fraction is the interest rate per compounding period.

這個分數就是每個複利週期的利率。

For a yearly interest rate of 4%, that compounds four times a year, the interest rate per compounding period is 1%.

如果年利率為 4%，每年複利四次，則每個複利期的利率為 1%。

And the exponent represents the number of times the interest has compounded.

指數代表複利計息的次數。

If it compounds four times per year and we leave it for two years, it'll compound a total of eight times.

如果每年複利四倍，我們把它放兩年，它總共會複利八倍。

We don't have to skip straight to the end, though.

不過，我們不必直接跳到結尾。

We can actually track the total amount every time it compounds.

實際上，我們可以跟蹤每次複合的總金額。

All we have to do is change the exponent to how many times it would have compounded at that point.

我們所要做的就是把指數改成當時的複利倍數。

After three months, it will compound for the first time.

三個月後，它將首次複合。

So we can just use an exponent of one to find that it will now have $1,010.

是以，我們只需使用 1 的指數，就可以計算出現在將有 1 010 美元。

After another three months, it compounds a second time.

又過了三個月，它又第二次復發了。

So the exponent is two.

所以指數是 2。

And now the account is up to $1,020.10.

現在賬戶餘額已達 1 020.10 美元。

Why don't you pause the video now and try filling in the remaining amounts in your notes?

現在請暫停視頻，然後在筆記中填寫剩餘的金額。

As the compounding periods continue, the value of the account continues to grow.

隨著複利期的持續，賬戶價值也在不斷增長。

Did you notice anything about how quickly it grows?

你注意到它生長得有多快了嗎？

Each time interest accrued, it was more than the last time.

每次產生的利息都比上次多。

This is why compound interest is so cool.

這就是複利如此美妙的原因。

It grows faster the longer you let it accrue.

時間越長，增長越快。

This is worth noting, however, that this is a pretty unrealistic example for a bank account.

但值得注意的是，這是一個非常不現實的銀行賬戶例子。

A bank simply isn't going to give you that much free money.

銀行根本不會給你那麼多閒錢。

A bank account would grow more like this.

銀行賬戶的增長會更像這樣。

Yeah, that's right.

是的，沒錯。

The bank will give you a whopping two cents every month.

銀行每個月會給你 2 美分。

Remember, banks are there to make money, so their savings accounts have super low interest rates.

請記住，銀行是為了賺錢，所以他們的儲蓄賬戶利率超低。

You're much more likely to find high interest rates on loans you borrow and have to pay back, like student loans or credit card loans.

您更有可能發現高利率出現在您借貸並必須償還的貸款上，如學生貸款或信用卡貸款。

In fact, let's do a little experiment with student loans.

事實上，讓我們用學生貸款做個小實驗。

Let's compare simple interest with compound interest.

讓我們來比較一下單利和複利。

Let's say you get a $5,000 loan your freshman year of college with a yearly interest rate of 5%, which you wait to start paying back until you graduate four years later.

假設你在大一的時候獲得了 5,000 美元的貸款，年利率為 5%，你要等到四年後畢業時才開始還貸。

Of course, compound interest has one extra variable to account for.

當然，複利還要考慮一個額外的變量。

So let's make it easy and say it only compounds once a year.

所以，讓我們簡單點，說它一年只發生一次。

With these terms, the simple interest loan will reach a total of $6,000 after four years, meaning it accrued $1,000 in interest.

按照這些條款，四年後單利貸款總額將達到 6 000 美元，這意味著它累計利息為 1 000 美元。

The compound interest, though, will come out to $77 more, and that's just with it compounding once a year.

不過，複利會多出 77 美元，這還只是每年一次的複利。

Most student loans actually compound daily.

大多數學生貸款實際上每天都在複利計算。

That's 365 times every year.

每年365次。

So a more realistic estimate for this loan would be $6,106.93, over $100 more than if it were simple interest.

是以，對這筆貸款更現實的估算是 6 106.93 美元，比單利多 100 多美元。

That's a lot of extra money you're paying on top of repaying the money you borrowed, and that's just for one semester of college.

除了償還借來的錢，你還要額外支付一大筆錢，而這僅僅是大學一個學期的學費。

Because of the speed at which compound interest grows, it's relatively easy to double the principal amount of an account that utilizes compound interest.

由於複利的增長速度很快，利用複利使賬戶本金翻番相對容易。

We can use the rule of 72 on any loan with compounding interest to estimate how long it will take to double in value.

我們可以利用任何複利貸款的 72法則來估算它的價值翻番需要多長時間。

The rule of 72 is pretty simple.

72 規則非常簡單。

You take 72 and divide it by the annual interest rate.

用 72 除以年利率。

Say the interest rate is 8%.

假設利率為 8%。

Then the value will double in approximately nine years.

大約九年後，價值將翻一番。

The complicated part of the rule of 72 is that it's most accurate around 8%.

72 定律的複雜之處在於，它在 8% 左右最為準確。

From there, every time the interest rate goes up by 3%, the number 72 should be increased by one.

此後，每當利率上升 3%，數字 72 就應增加 1。

If the interest rate increases another 3%, then the number on top grows by one again, and it's the same thing going the other way.

如果利率再增加 3%，那麼上面的數字又會增加 1，反之亦然。

Every 3% down is one less than 72.

每減少 3% 就比 72% 少一個。

Let's use the rule of 72 for this example.

在這個例子中，讓我們使用 72法則。

If an account has an interest rate of 3%, what number would we use on top?

如果一個賬戶的利率是 3%，我們在上面使用什麼數字？

3% is closer to 2% than to 5%, so we'll drop 72 twice down to 70.

3% 比 5% 更接近 2%，是以我們將 72 下降兩次，再下降到 70。

70 divided by three, since the interest rate is 3%, tells us this amount will double in approximately 23 years.

70 除以 3，因為利率是 3%，所以這筆錢在大約 23 年後將翻一番。

What about an interest rate of 15%?

那麼 15%的利率呢？

Pause the video now and try using the rule of 72 to find how long it will take to double.

現在暫停視頻，嘗試使用 72法則來計算翻倍需要多長時間。

15% is a little more than two jumps above 8%, so we'll bump the 72 up to 74, which means the value will double in about five years.

15%比 8%高出兩級多一點，是以我們將 72 提升到 74，這意味著大約五年後價值將翻一番。

If you're offered a loan with a 15% compounding interest rate, run away, quickly.

如果有人向你提供複利利率為 15%的貸款，那就趕緊跑路吧。

Because compound interest is way better for accounts where you're getting money, like savings accounts or investment returns, but for accounts where you're paying money back, like loans or credit cards, you'll end up paying less if it's simple interest.

因為複利更適合你獲得錢的賬戶，比如儲蓄賬戶或投資收益，但對於你還錢的賬戶，比如貸款或信用卡，如果是單利，你最終支付的利息會更少。

For a quick recap, simple interest is calculated using a simple formula.

簡單來說，單利的計算公式很簡單。

Compound interest uses a less simple formula with an extra variable for how often it compounds per year.

複利使用的公式不那麼簡單，每年複利的次數多了一個變量。

Simple interest is designed to grow at a steady rate for its term, while compound interest grows exponentially over time.

單利在其期限內以穩定的速度增長，而複利則隨著時間的推移呈指數增長。

For compound interest, you can use the rule of 72 to estimate how many years it will take to double the loan value.

對於複利，您可以使用 72法則來估算貸款價值翻番需要多少年。

But it's most accurate at around 8% interest, so you'll have to adjust it for higher or lower interest rates.

但它在利率為 8%左右時最為準確，是以您必須根據利率的高低進行調整。

As we continue through this financial literacy course, interest is going to come up a lot.

在我們繼續學習金融知識課程的過程中，利息會經常出現。

Now that you understand financial institutions and interest,

現在您瞭解了金融機構和利息、

I'd like to ask for your help.

我想請你幫忙。

Remember how my friend Caroline was having some money issues?

還記得我的朋友卡羅琳遇到的資金問題嗎？

I need your help comparing financial institutions in her city to find the best place for her to open a savings account.

我需要您幫助比較她所在城市的金融機構，以找到最適合她開設儲蓄賬戶的地方。

She's gonna owe us big time.

她會欠我們大人情的

See you next time.

下次再見

♪ Hey, hey ♪ ♪ Hey, hey ♪ ♪ Hey, hey ♪

嘿，嘿 嘿，嘿 嘿，嘿