Материал готовится,

пожалуйста, возвращайтесь позднее

пожалуйста, возвращайтесь позднее

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So let's generalize a bit

what we learned in the

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last presentation.

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Let's say I'm

borrowing P dollars.

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P dollars, that's what I

borrowed so that's my

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initial principal.

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So that's principal.

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r is equal to the rate,

the interest rate that

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I'm borrowing at.

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We can also write that

as 100r%, right?

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And I'm going to borrow

it for — well, I

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don't know — t years.

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Let's see if we can come up

with equations to figure out

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how much I'm going to owe at

the end of t years using either

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simple or compound interest.

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So let's do simple first

because that's simple.

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So at time 0 — so let's make

this the time axis — how

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much am I going to owe?

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Well, that's right when I

borrow it, so if I paid

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it back immediately, I

would just owe P, right?

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At time 1, I owe P plus the

interest, plus you can kind of

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view it as the rent on that

money, and that's r times P.

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And that previously, in the

previous example, in the

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previous video, was 10%.

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P was 100, so I had to pay $10

to borrow that money for a

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year, and I had to

pay back $110.

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And this is the same thing

as P times 1 plus r, right?

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Because you could

just use 1P plus rP.

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And then after two years,

how much do we owe?

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Well, every year, we just

pay another rP, right?

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In the previous example,

it was another $10.

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So if this is 10%, every

year we just pay 10% of

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our original principal.

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So in year 2, we owe P plus

rP — that's what we owed in

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year 1 — and then another

rP, so that equals

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P plus 1 plus 2r.

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And just take the P out,

and you get a 1 plus r

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plus r, so 1 plus 2r.

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And then in year 3, we'd owe

what we owed in year 2.

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So P plus rP plus rP, and then

we just pay another rP, another

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say, you know, if r is 10%, or

50% of our original principal,

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00:00:00,000 — > 00:00:00,000

2

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So let's generalize a bit

what we learned in the

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last presentation.

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Let's say I'm

borrowing P dollars.

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P dollars, that's what I

borrowed so that's my

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initial principal.

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So that's principal.

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r is equal to the rate,

the interest rate that

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I'm borrowing at.

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We can also write that

as 100r%, right?

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And I'm going to borrow

it for — well, I

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don't know — t years.

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00:00:25,051 — > 00:00:29,019

15

00:00:29,019 — > 00:00:32,021

Let's see if we can come up

with equations to figure out

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how much I'm going to owe at

the end of t years using either

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simple or compound interest.

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So let's do simple first

because that's simple.

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So at time 0 — so let's make

this the time axis — how

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much am I going to owe?

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Well, that's right when I

borrow it, so if I paid

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it back immediately, I

would just owe P, right?

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At time 1, I owe P plus the

interest, plus you can kind of

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view it as the rent on that

money, and that's r times P.

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And that previously, in the

previous example, in the

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previous video, was 10%.

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P was 100, so I had to pay $10

to borrow that money for a

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year, and I had to

pay back $110.

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And this is the same thing

as P times 1 plus r, right?

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Because you could

just use 1P plus rP.

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And then after two years,

how much do we owe?

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Well, every year, we just

pay another rP, right?

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In the previous example,

it was another $10.

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So if this is 10%, every

year we just pay 10% of

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our original principal.

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So in year 2, we owe P plus

rP — that's what we owed in

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year 1 — and then another

rP, so that equals

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P plus 1 plus 2r.

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And just take the P out,

and you get a 1 plus r

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plus r, so 1 plus 2r.

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And then in year 3, we'd owe

what we owed in year 2.

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So P plus rP plus rP, and then

we just pay another rP, another

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say, you know, if r is 10%, or

50% of our original principal,

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