Introduction to interest

well now you learn what I think is is is quite possibly one of the most useful concepts in life and then you might already be familiar with it but if you're not this will will hopefully keep you from one day filing for bankruptcy so anyway I will talk about interest and and then simple versus compound interest so what's interest interest we all have heard of it interest rates or interest on your mortgage or you know how much interest do I owe on my credit card so interest I don't know what the actual formal definition maybe I should look it up on Wikipedia but it's essentially rent on money so it's money that you pay in order to keep money for some period of time and that's probably not the most obvious definition but let me put it this way let's say that I want to borrow a hundred dollars from you so this is now and let's say that this is one year from now one year and this is you and this is me so now you give me $100 and then I have the hundred dollars and a year goes by and I have a hundred dollars here and if I were to just give you that hundred dollars back you would have collected no rent you would have just got your money back you would have collected no interest but if you said Sal I'm willing to give you a hundred dollars now if you give me I don't know if you give me a hundred and ten dollars a year later so in this situation how much did I pay you to keep that hundred dollars for a year well I'm paying you $10 more right I'm returning the hundred dollars I'm returning the hundred dollars and I'm returning another ten dollars and so this ten dollars this extra ten dollars that I'm returning to you is essentially the fee that I paid to be able to keep that money and do whatever I wanted with that money and maybe save it may be invested to whatever for a year and that ten dollars is essentially the interest and a way that it's often caught calculated is a percentage of the original amount that I borrowed and the original amount that I borrowed in phang fancy banker or finance terminology is just called principle principal principal so in this case the rent on the money or the interest was ten dollars and if I wanted to do it as a percentage I would say ten over the principal right which over 100 which is equal to ten percent so you might have said hey Sal I'm willing to pay I'm willing to lend you $1 $100 if you pay me 10 percent interest on it so 10 percent of $100 was ten dollars so after a year I pay you 100 plus the 10 percent and likewise so for any amount of money say you will you're willing to borrow lend me any amount of money for a 10 percent interest well then if you were to lend me a thousand dollars then the interest would be 10 percent of that which would be $100 so then after a year I would owe you a thousand plus 10 percent 10 percent times a thousand and that's equal to eleven hundred dollars right I just added in a zero to everything right in this case one hundred dollars would be the interest but it would still be ten percent so let me let me now make a distinction between simple interest and compound interest so we just did a fairly simple example where you lend money for me for a year at ten percent right so let's say that someone were to say that my interest rate interest rate that they charge or their interest rate they charge other people is well ten percent is a good number ten percent for a year and let's say I'm going to borrow I'm going to borrow the principle that I'm going to borrow from this person the principal I'm going to borrow is a hundred dollars so my question to you and maybe you want to pause it after I after I pose it is how much how much do I owe do I owe in ten years how much do I owe in ten years so there's really two ways of thinking about it you could say okay I start to see in years at time zero like if I just borrow the money I just paid it back immediately I'll just pay you know it'd be $100 right I'm not going to do that I'm going to keep it for at least a year so after a year just based on the example that we just did I could add 10% of that amount to the hundred dollars and it would then I would then owe 110 dollars and then after two years I could add another 10% of the original principle right so every year I'm just adding ten dollars so in this case would be $120 and in year three I would have $130 essentially my rent per year to borrow this hundred dollars is ten dollars right because I'm always taking 10% of the original amount and after after ten years because I would each year out of had to pay an extra ten dollars in interest after ten years I would owe $200 right and that $200 is equal to a hundred dollars of principal principal plus $100 of interest because I paid ten dollars a year of interest and this notion in which I just did here this is actually called simple simple interest which is essentially you take the original amount you borrowed the interest rate the amount the the fee that you pay every year is the interest rate times that original amount and you just incrementally pay that every year but if you think about it you're actually paying a smaller and smaller percentage of what you owe going into that year and maybe when I show you compound interest that'll make sense so this is one way to interpret ten percent interest a year another way to interpret it is okay so in Year Zero right you still you know it's 100 dollars that you're borrowing or if you just if they had the money they said oh no no I don't want it you just paid back you two $100 after a year you would essentially pay the hundred dollars plus ten percent of $100 right which is one hundred and ten dollars so that's one hundred plus ten percent of 100 let me switch colors because it's monotonous right but I think this make sense to you and this is where a simple and compound interest starts to diverge and the last situation we just kept adding 10% of the original hundred dollars in compound interest in compound interest now we don't take 10% of the original amount we now take 10% of this amount right and so what are we doing every every so now we're going to take the original we're going to take $110 it's going to be our new you can almost view it as our new principal it's like we this is how much we offer a year and then we would rebar oh it right so now we're going to $110 plus 10% times 110 right and that is equal to you could actually undistribute 110 out and that equal that's equal to 110 times 110 you can you can actually actually actually 110 times 1.1 right and so that equals and actually I could rewrite it this way is - I could rewrite is 100 times 1.1 squared and that equals what's 121 dollars and then in year 2 this is my new principle this 121 this is my new principle and now I have to in year 3 so this is year - I'm taking more space so this is year - and now in year 3 I'm going to have to pay 120 $1 that I owed at the end of year 2 plus 10% times the amount of money I owed going into the year 121 dollars and if we and so that's the same thing we could put parentheses around here so that's the same thing as 1 times 121 plus point one times 121 so that's the same thing as 1 point 1 times 121 or another way of viewing it that's equal to our original principal times 1 point 1 to the 3rd power and if you keep doing this and I encourage you to do it because it'll really give you a hands-on sense at the end of ten years we will owe or you I forgot who's borrowing from whom a hundred dollars times one point one to the tenth power and what is that equal let me get my spreadsheet out just pick a random cell the plus one hundred times one point one to the tenth power so two hundred and fifty nine dollars and some change two hundred and fifty nine dollars so it might seem like a very subtle distinction but it ends up being a very big difference when I compounded at ten percent for ten years what for ten years using compound interest I owe two hundred fifty nine dollars when when I did it using simple interest I only owed two hundred dollars so that fifty nine dollars was kind of the increment of how much more compound interest cost me I'm about to run out of time so I'll do a couple of more examples in the next video just so you really get a deep understanding of how do you compound interest how the exponents work and and and what really is the difference I'll see in the next video