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  • They say, 'Time is money,'

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

  • Meet Sheila!

  • She just got her first big bonus.

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

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

  • Yes, Sheila, that's a nice car!

  • Oh, looks like Sheila is a little short.

  • But wait!

  • She has an idea.

  • Sheila is a smart cookie.

  • She knows that if she deposits the money for a year

  • instead of buying the car today,

  • she will earn interest.

  • Then she'll be able to afford the car.

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

  • will equal the money deposited today plus the interest earned.

  • We call Sheila's money deposited today

  • the present value of money.

  • And the value of Sheila's deposit next year

  • is the future value of money.

  • What connects one to the other?

  • The interest rate,

  • also known as the time value of money.

  • Now, with a little bit of rearranging,

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

  • with this equation.

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

  • Well, it's been a year!

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

  • Sheila really understands the future value of money.

  • Now, I just hope she understands the speed limit!

  • Now, meet Timmy.

  • He's also gotten his bonus.

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

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

  • Oh! Looks like you're a little short.

  • Maybe you can follow Sheila's example.

  • You see, Timmy, just like Sheila,

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

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

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

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

  • With a little bit of rearranging,

  • it becomes the value of your money next year,

  • times one plus the interest rate.

  • We can then convert the future value one year from now

  • to the present value times one plus the interest rate.

  • We can even simplify this further

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

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

  • but you still can't afford the car!

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

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

  • Do you see that little number two in the equation?

  • Any number that you put in there

  • is the number of years that you are waiting,

  • also known as the period.

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

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

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

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

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

  • 10 years?

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

  • Not quite.

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

  • You should ask Sheila for a ride to the beach.

  • Maybe a bicycle will suit you better?

  • I hear the bus is pretty cheap!

They say, 'Time is money,'

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A2 TED-Ed sheila timmy interest rate interest deposited

【TED-Ed】The time value of money - German Nande

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    稲葉白兎 posted on 2014/11/30
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