e and compound interest발음듣기
대기중
e and compound interest
120문장
98%
베트남어 번역 1명 참여
출처 : 칸아카데미
번역
0%
So you come to me the local loan shark, and you say hey I need to borrow a dollar for a year. I tell you I'm in a good mood, I willing to lend you that dollar that you need for a year. I will lend it to you for the low interest of 100% per year. 100% per year.발음듣기
대기중
You're going to have to pay the original principal what I lent you plus 100% of that. Plus one other dollar.발음듣기
대기중
Which is clearly going to be equal to $2. You say oh gee, that's a lot to have to pay to pay back twice what I borrowed.발음듣기
대기중
I say oh gee, if your willing to pay back in 6 months, then I'll just charge you half the interest for half the time.발음듣기
대기중
How much would you have to pay? Well, you would have to pay the original principal what you borrowed.발음듣기
대기중
What I'll do is just say that okay, you don't have the money for me yet. I'll essentially ... we could think about it.발음듣기
대기중
I will just lend that amount that you need for you for another 6 months. We'll lend that out.발음듣기
대기중
We'll lend that out for another 6 months at the same interest rate at 50% for the next 6 months.발음듣기
대기중
Another way of thinking about it is to go from $1 over the first period, you just multiply that times 1.5. If your going to grow something by 50%, you just multiply it times 1.5.발음듣기
대기중
Multiplying by 1.5. If you start with 1 and multiply by 1.5 twice, this is going to be the same thing.발음듣기
대기중
This is the same thing. 100% is the same thing as multiplying by 2. As we be multiplying 1 plus 1.발음듣기
대기중
1 times 1 to the first ... I'm sorry 1 times 2 to the first power , because your only doing it over one period over that year.발음듣기
대기중
You say once again where's that 2? Well, if someone is asking for 100%, that means over the period you're going have to pay twice.발음듣기
대기중
If someone is charging you 50% over every period, you're going have to pay whatever you borrowed.발음듣기
대기중
If you wanted to see how this actually related to the interest, you could view this as ... this right over here is equal to 1 times, the interest part is 1 plus 100% divided by 1 period to the first power.발음듣기
대기중
Writing 1 plus 1, but you'll see that we can keep writing this as we compound over different periods.발음듣기
대기중
Each of them at 50%. 1 plus 100% over 2 is the same thing as 1.5, and we compounded it over 2 periods.발음듣기
대기중
This is $2.25. That was more than the original $2, so you say, well what if we do this over every 12 months. I say, "Sure. We got a program for that."발음듣기
대기중
After every 12 months ... or after every month I should say, I'm just going to charge you 100% divided by 12 interest.발음듣기
대기중
Having to pay back the principal plus 8 1/3%, that's the same thing as multiplying times 1.083 repeating.발음듣기
대기중
And this isn't the scale that actually looks more than 2 months, but it's not completely at scale.발음듣기
대기중
What's the total interest you would have to pay over a year if you weren't able to keep coming up with the money?발음듣기
대기중
If you wanted to write it in this form right over here, this would be the same thing as the original principal.발음듣기
대기중
Our original principal times 1 plus 100% divided by 12. Now we've divided our 100% into 12 periods, and we're going to compound that 12 times.발음듣기
대기중
I just did that there to kind of hopefully you'd see the kind of structure in this expression.발음듣기
대기중
So approximately 2.613. You say well this is an interesting game you all most forgot about your financial troubles, and you're just intrigued by what happens if we keep going this.발음듣기
대기중
If I borrowed a one dollar, and I'd say well gee I'm just going to ... each day I'm going to charge you charge you one three hundred sixty-fifth of a 100%.발음듣기
대기중
So, 100% divided 365, and I'm going to compound that 365 times. You're curious mathematically.발음듣기
대기중
You're going to have your original principal times 1 plus 100% divided by not 12. Now we've divided the 100% into 365 periods.발음듣기
대기중
Every time we have to multiply by 1 plus 100% over 365 everyday that the loan is not paid. 365th power.발음듣기
대기중
Then you say well maybe not so bad, because 100% divided by 365 is going to be a small number.발음듣기
대기중
This is the same thing as 1 plus. 100% is the same thing as 1 divided by 365 to the 365th power.발음듣기
대기중
Then we get ... This is approximately equal to ... this approximate is a very precise approximation, but 2.7 ...발음듣기
대기중
It looks as if we take larger and larger numbers here, it just doesn't just balloon into some crazy ginormous number.발음듣기
대기중
If you were to take your 100% and divide by larger and larger numbers, but take it to that power, you're going to approach perhaps the most magical and mystical number of all.발음듣기
대기중
I can do that, so E to the ... I'll raise it to the first power so you can look at the calculators internal representation of it.발음듣기
대기중
You see all ready raising some ... doing 1 plus 1 over 365 to the 365th power, we got pretty ... we're starting to get really really close to E. I encourage you try this with larger and larger numbers, and your going to get closer and closer to this magical mystery.발음듣기
대기중
칸아카데미 더보기더 보기
-
Monopolist Optimizing Price (part 3)- Dead We...
68문장 0%번역 좋아요1
번역하기 -
Maurice Ravel. Daphnis et Chloé. Analysis by...
68문장 0%번역 좋아요1
번역하기 -
China keeps peg but diversifies holdings
35문장 0%번역 좋아요0
번역하기 -
Mussolini becomes Prime Minister
62문장 0%번역 좋아요0
번역하기
