If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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