Growing by a percentage Growing a quantity by a percentage
Growing by a percentage
⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles.
- Let's do some more percentage problems.
- Let's say that I start this year in my stock
- portfolio with $95.00.
- And I say that my portfolio grows by, let's say, fifteen percent.
- How much do I have now?
- I think you might be able to figure this out on your own,
- but of course we'll do some example problems, just in case
- it's a little confusing.
- So I'm starting with $95.00, and I'll get rid of
- the dollar sign.
- We know we're working with dollars.
- ninety-five dollars, right?
- And I'm going to earn, or I'm going to grow just because
- I was an excellent stock investor, that ninety-five dollars
- is going to grow by fifteen percent.
- So to that ninety-five dollars, I'm going to add another fifteen percent of ninety-five.
- So we know we write 15% as a decimal, as 0.15, so 95 plus
- 0.15 of 95, so this is times 95-- that dot
- is just a times sign.
- It's not a decimal, it's a times, it's a little higher
- than a decimal-- So 95 plus 0.15 times 95 is what
- we have now, right?
- Because we started with ninety-five dollars, and then we made
- another fifteen percent times what we started with.
- Hopefully that make sense.
- Another way to say it, the ninety-five dollars has grown by fifteen percent.
- So let's just work this out.
- This is the same thing as 95 plus-- what's 0.15 times 95?
- Let's see.
- So let me do this, hopefully I'll have enough space here.
- 95 times 0.15-- I don't want to run out of space.
- Actually, let me do it up here, I think I'm about to run out
- of space-- 95 times 0.15.
- five times five is twenty-five, nine times five is forty-five plus two is forty-seven, one times ninety-five is
- ninety-five, bring down the five, twelve, carry the one, fifteen.
- And how many decimals do we have?
- one, two.
- Actually, is that right?
- I think I made a mistake here.
- See five times five is twenty-five.
- five times nine is forty-five, plus two is forty-seven.
- And we bring the zero here, it's ninety-five, one times five, one times nine, then
- we add five plus zero is five, seven plus five is twelve-- oh.
- I made a mistake.
- It's 14.25, not 15.25.
- So I'll ask you an interesting question?
- How did I know that 15.25 was a mistake?
- Well, I did a reality check.
- I said, well, I know in my head that fifteen percent of one hundred is fifteen, so if
- fifteen percent of one hundred is fifteen, how can fifteen percent of ninety-five be more than fifteen?
- I think that might have made sense.
- The bottom line is ninety-five is less than one hundred.
- So fifteen percent of ninety-five had to be less than fifteen, so I knew my
- answer of 15.25 was wrong.
- And so it turns out that I actually made an addition
- error, and the answer is 14.25.
- So the answer is going to be ninety-five plus fifteen percent of ninety-five, which is the
- same thing as 95 plus 14.25, well, that equals what?
- Notice how easy I made this for you to read,
- especially this two here.
- So if I start off with $95.00 and my portfolio grows-- or the
- amount of money I have-- grows by fifteen percent, I'll end
- up with $109.25.
- Let's do another problem.
- Let's say I start off with some amount of money, and after a
- year, let's says my portfolio grows twenty-five percent, and after growing
- twenty-five percent, I now have $one hundred.
- How much did I originally have?
- Notice I'm not saying that the $one hundred is growing by twenty-five percent.
- I'm saying that I start with some amount of money, it grows
- by twenty-five percent, and I end up with $one hundred after it grew by twenty-five percent.
- To solve this one, we might have to break out
- a little bit of algebra.
- So let x equal what I start with.
- So just like the last problem, I start with x and it grows by
- twenty-five percent, so x plus twenty-five percent of x is equal to one hundred, and we know this
- 25% of x we can just rewrite as x plus 0.25 of x is equal to
- one hundred, and now actually we have a level-- actually this might be
- level three system, level three linear equation-- but the bottom
- line, we can just add the coefficients on the x.
- x is the same thing as onex, right?
- So 1x plus 0.25x, well that's just the same thing as 1 plus
- 0.25, plus x-- we're just doing the distributive property
- in reverse-- equals one hundred.
- And what's 1 plus 0.25?
- That's easy, it's 1.25.
- So we say 1.25x is equal to 100.
- Not too hard.
- And after you do a lot of these problems, you're going to
- intuitively say, oh, if some number grows by twenty-five percent, and it
- becomes 100, that means that 1.25 times that number
- is equal to one hundred.
- And if this doesn't make sense, sit and think about it a little
- bit, maybe rewatch the video, and hopefully it'll, over time,
- start to make a lot of sense to you.
- This type of math is very very useful.
- I actually work at a hedge fund, and I'm doing
- this type of math in my head day and night.
- So 1.25 times x is equal to 100, so x would equal
- 100 divided by 1.25.
- I just realized you probably don't know
- what a hedge fund is.
- I invest in stocks for a living.
- Anyway, back to the math.
- So x is equal to 100 divided by 1.25.
- So let me make some space here, just because I
- used up too much space.
- Let me get rid of my little let x statement.
- Actually I think we know what x is and we know
- how we got to there.
- If you forgot how we got there, you can I guess
- rewatch the video.
- Let's see.
- Let me make the pen thin again, and go back to
- the orange color, OK.
- X equals 100 divided by 1.25, so we say 1.25 goes into
- 100.00-- I'm going to add a couple of 0's, I don't know how
- many I'm going to need, probably added too many-- if I
- move this decimal over two to the right, I need to move this
- one over two to the right.
- And I say how many times does one hundred go into one hundred-- how many
- times does one hundred and twenty-five go into one hundred?
- How many times does it go into one thousand?
- It goes into it eight times.
- I happen to know that in my head, but you could do trial
- and error and think about it.
- eight times-- if you want to think about it, eight times one hundred is
- eight hundred, and then eight times twenty-five is two hundred, so it becomes one thousand.
- You could work out if you like, but I think I'm running out of
- time, so I'm going to do this fast.
- eight times one hundred and twenty-five is one thousand.
- Remember this thing isn't here.
- one thousand, so one thousand minus one thousand is zero, so you can bring down the zero.
- one hundred and twenty-five goes into zero zero times, and we just keep getting zero's.
- This is just a decimal division problem.
- So it turns out that if your portfolio grew by twenty-five percent and
- you ended up with $100.00 you started with $80.00.
- And that makes sense, because twenty-five percent is roughly one / four, right?
- So if I started with $80.00 and I grow by 1/4, that means I
- grew by $twenty, because twenty-five percent of eighty is twenty.
- So if I start with eighty and I grow by twenty,
- that gets me to one hundred.
- Makes sense.
- So remember, all you have to say is, well, some number times
- 1.25-- because I'm growing it by 25%-- is equal to 100.
- Don't worry, if you're still confused, I'm going to add at
- least one more presentation on a couple of more
- examples like this.
Be specific, and indicate a time in the video:
At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger?
Have something that's not a question about this content?
This discussion area is not meant for answering homework questions.
Share a tip
When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831...
Have something that's not a tip or feedback about this content?
This discussion area is not meant for answering homework questions.
Discuss the site
For general discussions about Khan Academy, visit our Reddit discussion page.
Flag inappropriate posts
Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians.
- disrespectful or offensive
- an advertisement
- low quality
- not about the video topic
- soliciting votes or seeking badges
- a homework question
- a duplicate answer
- repeatedly making the same post
- a tip or feedback in Questions
- a question in Tips & Feedback
- an answer that should be its own question
about the site