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Let's do some more percentage problems.

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Let's say that I start this year in my stock

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portfolio with $95.00.

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And I say that my portfolio grows by, let's say, 15%.

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How much do I have now?

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OK.

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I think you might be able to figure this out on your own,

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but of course we'll do some example problems, just in case

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it's a little confusing.

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So I'm starting with $95.00, and I'll get rid of

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the dollar sign.

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We know we're working with dollars.

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95 dollars, right?

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And I'm going to earn, or I'm going to grow just because

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I was an excellent stock investor, that 95 dollars

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is going to grow by 15%.

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So to that 95 dollars, I'm going to add another 15% of 95.

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So we know we write 15% as a decimal, as 0.15, so 95 plus

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0.15 of 95, so this is times 95-- that dot

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is just a times sign.

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It's not a decimal, it's a times, it's a little higher

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than a decimal-- So 95 plus 0.15 times 95 is what

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we have now, right?

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Because we started with 95 dollars, and then we made

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another 15% times what we started with.

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Hopefully that make sense.

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Another way to say it, the 95 dollars has grown by 15%.

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So let's just work this out.

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This is the same thing as 95 plus-- what's 0.15 times 95?

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Let's see.

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So let me do this, hopefully I'll have enough space here.

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95 times 0.15-- I don't want to run out of space.

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Actually, let me do it up here, I think I'm about to run out

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of space-- 95 times 0.15.

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5 times 5 is 25, 9 times 5 is 45 plus 2 is 47, 1 times 95 is

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95, bring down the 5, 12, carry the 1, 15.

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And how many decimals do we have?

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1, 2.

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15.25.

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Actually, is that right?

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I think I made a mistake here.

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See 5 times 5 is 25.

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5 times 9 is 45, plus 2 is 47.

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And we bring the 0 here, it's 95, 1 times 5, 1 times 9, then

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we add 5 plus 0 is 5, 7 plus 5 is 12-- oh.

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See?

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I made a mistake.

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It's 14.25, not 15.25.

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So I'll ask you an interesting question?

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How did I know that 15.25 was a mistake?

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Well, I did a reality check.

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I said, well, I know in my head that 15% of 100 is 15, so if

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15% of 100 is 15, how can 15% of 95 be more than 15?

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I think that might have made sense.

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The bottom line is 95 is less than 100.

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So 15% of 95 had to be less than 15, so I knew my

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answer of 15.25 was wrong.

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And so it turns out that I actually made an addition

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error, and the answer is 14.25.

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So the answer is going to be 95 plus 15% of 95, which is the

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same thing as 95 plus 14.25, well, that equals what?

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109.25.

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Notice how easy I made this for you to read,

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especially this 2 here.

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109.25.

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So if I start off with $95.00 and my portfolio grows-- or the

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amount of money I have-- grows by 15%, I'll end

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up with $109.25.

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Let's do another problem.

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Let's say I start off with some amount of money, and after a

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year, let's says my portfolio grows 25%, and after growing

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25%, I now have $100.

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How much did I originally have?

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Notice I'm not saying that the $100 is growing by 25%.

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I'm saying that I start with some amount of money, it grows

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by 25%, and I end up with $100 after it grew by 25%.

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To solve this one, we might have to break out

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a little bit of algebra.

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So let x equal what I start with.

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So just like the last problem, I start with x and it grows by

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25%, so x plus 25% of x is equal to 100, and we know this

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25% of x we can just rewrite as x plus 0.25 of x is equal to

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100, and now actually we have a level-- actually this might be

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level 3 system, level 3 linear equation-- but the bottom

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line, we can just add the coefficients on the x.

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x is the same thing as 1x, right?

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So 1x plus 0.25x, well that's just the same thing as 1 plus

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0.25, plus x-- we're just doing the distributive property

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in reverse-- equals 100.

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And what's 1 plus 0.25?

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That's easy, it's 1.25.

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So we say 1.25x is equal to 100.

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Not too hard.

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And after you do a lot of these problems, you're going to

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intuitively say, oh, if some number grows by 25%, and it

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becomes 100, that means that 1.25 times that number

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is equal to 100.

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And if this doesn't make sense, sit and think about it a little

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bit, maybe rewatch the video, and hopefully it'll, over time,

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start to make a lot of sense to you.

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This type of math is very very useful.

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I actually work at a hedge fund, and I'm doing

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this type of math in my head day and night.

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So 1.25 times x is equal to 100, so x would equal

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100 divided by 1.25.

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I just realized you probably don't know

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what a hedge fund is.

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I invest in stocks for a living.

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Anyway, back to the math.

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So x is equal to 100 divided by 1.25.

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So let me make some space here, just because I

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used up too much space.

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Let me get rid of my little let x statement.

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Actually I think we know what x is and we know

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how we got to there.

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If you forgot how we got there, you can I guess

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rewatch the video.

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Let's see.

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Let me make the pen thin again, and go back to

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the orange color, OK.

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X equals 100 divided by 1.25, so we say 1.25 goes into

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100.00-- I'm going to add a couple of 0's, I don't know how

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many I'm going to need, probably added too many-- if I

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move this decimal over two to the right, I need to move this

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one over two to the right.

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And I say how many times does 100 go into 100-- how many

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times does 125 go into 100?

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None.

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How many times does it go into 1000?

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It goes into it eight times.

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I happen to know that in my head, but you could do trial

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and error and think about it.

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8 times-- if you want to think about it, 8 times 100 is

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800, and then 8 times 25 is 200, so it becomes 1000.

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You could work out if you like, but I think I'm running out of

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time, so I'm going to do this fast.

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8 times 125 is 1000.

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Remember this thing isn't here.

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1000, so 1000 minus 1000 is 0, so you can bring down the 0.

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125 goes into 0 zero times, and we just keep getting 0's.

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This is just a decimal division problem.

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So it turns out that if your portfolio grew by 25% and

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you ended up with $100.00 you started with $80.00.

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And that makes sense, because 25% is roughly 1/4, right?

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So if I started with $80.00 and I grow by 1/4, that means I

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grew by $20, because 25% of 80 is 20.

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So if I start with 80 and I grow by 20,

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that gets me to 100.

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Makes sense.

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So remember, all you have to say is, well, some number times

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1.25-- because I'm growing it by 25%-- is equal to 100.

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Don't worry, if you're still confused, I'm going to add at

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least one more presentation on a couple of more

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examples like this.

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