Name: 興趣 - 青少年金融知識！ (Interest - Financial Literacy for Teens!)
Uploaded: 2024-09-10T19:50:19.000Z
Duration: 15 min 37 s

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。

基礎被動語態

But one big question was left unanswered.

但有一個大問題沒有得到解答。

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。

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。

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

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.

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.

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。

讓我們來看看這方面的一些例子。

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.

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.

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。

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

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

Okay, so most of the variables are the same.

好吧，大部分變量都是一樣的。

這個出現兩次的 N 又是怎麼回事？

That's a major part of compound interest.

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

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 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。

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.

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.

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。

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.

This is why compound interest is so cool.

It grows faster the longer you let it accrue.

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.