let's do some more percentage problems
let's say that I start this year in my
stock portfolio with $95 and I say that
my portfolio portfolio grows by let's
say fifteen percent how much do I have
now have now okay 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 and I'll get rid
of the dollar sign we know it working
with dollars $95 right and I'm going to
earn I'm going to grow just because I
was an excellent stock investor I that
$95 is going to grow by 15% so to that
$95 I'm going to add another 15% of 95
so we know we write fifteen percent as a
decimal as 0.15 so 95 plus 0.15 of 95
plus times 95 that dot is just a time
sign it's not a decimal two 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 $95 and then we
made another 15% times what we started
with hopefully that makes sense another
way we say the $95 has grown by 15% 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 it hopefully I
have enough space here 95 is 0.15 I
don't want to run out of space so let me
do it up here I think I'm about to run
out of space 95
times 0.15 5 times 5 is 25 9 times 5 is
45 plus 2 is 47 1 times 95 is 95 bring
down the 5 12 carry the 1 15 and how
many decimals do we have 1 2
15 point 2 5 choose that right I think I
made a mistake here see 5 times 5 is 25
5 times 9 is 45 plus 2 is 47 now we're
putting a 0 here it's 95 right 1 times 5
1 times 9 and then we add 5 plus 0 is 5
7 plus 5 is 12 Oh see I made a mistake
it's 14 point two five not 15 point 2 5
so I'll ask you an interesting question
how did I know that that fifteen point
two five was a mistake well I did a
reality check
I said well I know in my head that 15
percent of a hundred is 15 so 15 percent
of a hundred is 15 how can 15 percent of
95 be more than 15 I think that might
have made sense I the bottom line is 95
is less than 100 so 15 percent of 95 had
to be less than 15 so I knew my answer
15 point two five was wrong and so it
turns out that I actually made an
addition error and the answer is 14
point two five so the answer is going to
be 95 plus 15% of 95 which is the same
thing as 95 plus fourteen point two five
so 95 plus fourteen point two five well
that equals what 109 point two five one
hundred and nine point two five notice
how easy I made this for you to read
especially this two here one hundred
nine point two five so if I start off
with 95 dollars and my portfolio grows
or the amount of money I have grows by
15% I'll end up with a hundred and nine
dollars and a quarter
let's do another problem let's say I
start off with some amount of money and
after a year let's see I my portfolio
grows my portfolio grows 25% and after
after growing 25%
I now have let's say I now have $100 how
much did I originally have notice I'm
not saying that the hundred dollars is
growing by 25% I'm saying that I start
with some amount of money it grows by
25% and I end up with $100 after it grew
by 25% to solve this one we might have
to break out a little bit of algebra so
let X equal what I start with
what I start with so just like the last
problem I start with X and it grows by
25% so X plus 25% of X is equal to 100
and we know this 25% of X we can just
rewrite as X plus 0.25 of X is equal to
100 and now actually we have a level
actually this might be a level 3 system
level 3 a linear equation but the bottom
line we could just add the coefficients
on the X so here we X is the same thing
as 1x right so 1x plus 0.25 X well
that's just the same thing as 1 plus
0.25 X we're just doing the distributive
property in Reverse equals 100 and
what's what what's 1 plus 0.25 and it's
easy it's 1.25 so they say 1.25 X is
equal to 100 not too hard and after you
do a lot of these problems you're going
to
to ative lycée oh if some number grows
by 25% and it becomes 100 that means
that 1.25 times that number is equal to
100 and if this doesn't make sense sit
and think about it a little bit maybe
Yuri watch the video and and and
hopefully it'll over time start to make
a lot of sense to you and this is not
this type of math is very very useful I
actually I 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 one hundred 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 we know what X is and we know
how we got to the there if you forgot
how we got there you can I guess we
watched the video let's see let me make
the pen then again and go back to the
orange color ok x equals 100 divided by
1.25 so we say 1.25 goes into 100 point
zero zero I'm gonna add a couple of zero
I don't know how many I'm going to need
I provided too many
if I move this decimal over two to the
right I need to move this one over two
to the right right and I say well how
many times is 100 100 how many times is
125 go into 100 none how many times does
it go into a 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 what eight times 100 is
800 and then eight times 25 is 200 so it
becomes 1,000 you could work it out if
you like but I think I'm running out of
time so I'm gonna do this fast
eight times 125 is 1,000 remember this
this thing isn't here
1,000 so one thousand - thousand is zero
so you can bring down to zero 125 goes
into 0 zero times and we just keep
getting zeroes this is just a decimal
division problem so it turns out that if
your portfolio grew by 25% and you ended
up with $100 you started with $80 and
that makes sense because 25% is roughly
1/4 right so if I start with $80 and I
grow by 1/4 that means I grew by 20
dollars because 25 percent of 80 is 20
so if I start with 80 and I grow by 20
that gets me to 100 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 your constancy I'm going to add
at least one more presentation on a
couple of more examples like this