but what does one really have to do with the other?

但時間跟金錢到底怎麼扯上關係？

Meet Sheila!

我們來看看希拉的例子。

She just got her first big bonus.

她剛得到生平第一筆大獎金。

Sheila knows exactly what she wants to do with that money.

希拉早就決定好怎麼用這筆錢。

She's had her eye on a nice convertible for a while now.

她看中一輛敞篷車好一陣子。

Yes, Sheila, that's a nice car!

果然，這車真不賴。

Oh, looks like Sheila is a little short.

但看起來有點超出預算。

But wait!

等等。

She has an idea.

她有別的主意。

Sheila is a smart cookie.

希拉是聰明人。

She knows that if she deposits the money for a year

她知道如果把錢存在銀行一年，

instead of buying the car today,

不要現在籌錢買車，

she will earn interest.

她就可以靠存款賺點利息。

Then she'll be able to afford the car.

這樣就買得起車。

Sheila knows that the value of her deposit one year from now

她知道一年後她的存款

will equal the money deposited today plus the interest earned.

會是她現有的本金加上利息。

We call Sheila's money deposited today

一般稱當下存入的金額

the present value of money.

為現值。

And the value of Sheila's deposit next year

而明年席拉的存款

is the future value of money.

則稱為終值。

What connects one to the other?

兩者之間怎麼計算？

The interest rate,

由利率來計算。

also known as the time value of money.

也稱為金錢的時間價值。

Now, with a little bit of rearranging,

稍微整理一下式子，

we can figure out the future value of Sheila's money

就能從等式中看出

with this equation.

希拉存款的終值。

So in a year, the future value will be $11,000.

一年後，終值會是11,000美金。

Well, it's been a year!

一年後，我們再來看看希拉。

And there's Sheila, with enough money to buy the car.

現在她有充裕的錢買車。

Sheila really understands the future value of money.

她完全掌握終值的概念。

Now, I just hope she understands the speed limit!

現在只希望她能多注意一下速限。

Now, meet Timmy.

再拿提米當作例子。

He's also gotten his bonus.

他也得到一筆獎金。

The money seems to be burning a hole in his pocket.

等不及想大肆採購。

Yes, Timmy, that's a nice car that will surely impress people.

沒錯，那肯定是會羨煞眾人的好車。

Oh! Looks like you're a little short.

但看樣子錢有點不足。

Maybe you can follow Sheila's example.

或許可以效仿希拉的例子。

You see, Timmy, just like Sheila,

提米就像希拉一樣，

after the first year, you'll have $11,000.

一年後，他就可以有11,000美金。

But Timmy, that is still not enough to buy that fancy car.

但這樣還是買不起那輛高檔車。

Why don't you leave the money deposited for another year?

或許他可以多等一年。

Let's see how your deposit will be doing in two years.

看看兩年後，存款會有什麼樣的變化。

With a little bit of rearranging,

整理式子，

it becomes the value of your money next year,

可以看出兩年後的存款金額，

times one plus the interest rate.

等於明年的存款金額乘上一加利率。

We can then convert the future value one year from now

明年的存款金額也可以說是

to the present value times one plus the interest rate.

現值乘以一加利率。

We can even simplify this further

簡化式子可以得出

by just squaring the value of one plus the interest rate.

現值乘以一加利率的平方。

Sorry, Timmy, you'll have more money after two years,

可惜的是，雖然兩年後提米的錢變多，

but you still can't afford the car!

但還是買不起車。

I don't know how many more years you'll have to wait,

不知道他還需要等多少年，

but I can tell you one way we can figure it out.

但有個方法能找到答案。

Do you see that little number two in the equation?

有看到等式上小小的二嗎？

Any number that you put in there

那個位置的數字

is the number of years that you are waiting,

就代表還需要等幾年。

also known as the period.

也稱為期數。

Sure, Timmy, we can see how much you'll have in five years.

因此可以算算五年後，提米會有多少錢。

Let's connect future value and present value across five years.

來看看五年後終值跟現值的差距。

Let's watch the period increase from two to five.

當期數從二調到五，

After 5 years, you'll have $16,105.10.

五年後，會有16,105.10美金。

Sorry, Timmy, you have to wait a little longer.

很抱歉，還需要再多等幾年。

10 years?

十年呢？

Yeah! Let's see if you'll be able to buy the car then.

來看看錢夠了沒。

Not quite.

還差一點。

Well, Timmy, it looks like you'll need 26 years to afford this car.

看起來提米需要等二十六年才能買得起這輛車。

You should ask Sheila for a ride to the beach.

不如直接請希拉載他一程到海邊比較快。

Maybe a bicycle will suit you better?

也可能買台腳踏車比較合適？

I hear the bus is pretty cheap!

還有公車也是個實惠的選擇。