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Intro to compound interest

Let's understand how compound interest is different from simple interest. Let's also see how compound interest is simply a special case of percentage increase. Created by Aanand Srinivas.

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Video transcript

let's understand compound interest a good place to begin is actually simple interest now you mean remember what simple interest is but if I had to summarize simple interest and in fact both simple interest and compound interest in just one line all I'll say is simple interest is where you charge interest just on the principle as many years past you don't do anything the principle remains the same in compound interest as the years go by you start charging interest also on the interest in other words the principle keeps growing that's it I know that's a one line somebody and that's not enough so let's jump in let's look at an example it's let's imagine that you have thousand rupees and you decide to give the bank a loan of this talk and rupees are you can give the banker loan rate that that's what we call in deposit so you give the bank alone maybe you decide to keep it for three years now the bank says that I'm gonna give you ten percent for this thousand rupees that you give me every year so we have a big way of saying that we say the bank is giving you ten percent per annum you know percentage rate basically this is given gonna give you ten percent of this thousand for every year that you let them keep this money now what does that mean it means that after a year passes they owe you not just a thousand rupees they owe you 100 rupees more so they're gonna give you thousand rupees and hundred and why is it hundred because finding ten percent of thousand is gonna be easy ten percent of thousand is just thousand divided by 10 so it's hundred now what's gonna happen after one more you are things gonna change a lot not really right everything remains the same the principles the same so I think what nothing much happens so let's just see what's gonna happen so let's take this again let's go here and let's see what happens so nothing much is changed your number one has passed except over here it's your number two now so it's your number two same 10% same principle of thousand same hundred rupee interest let's do this again for the third year okay nothing's gonna change you can see how predictable this is which is why finding simple interest is really simple just have to multiply the interest that you get for one year by as many years as you have and you'll get the answer so you have you're number one you're number two and you're number three have passed how much money will you have totally at the end of this you can notice that you're gonna have your original thousand they can't take that away from you and then you have one hundred one hundred hundred for the three years so that's going to be thousand plus three hundred thousand three hundred would be and that's a good deal you got 300 rupees when you do this this is called simple interest the principle does not change but I have a question for you the question I have is will you take this deal now it seems like a good deal but if you watch closely you can actually find a clever way to make more money in the same of the same conditions and let's see what that is let's bring this down over here and let's see what we can do so there is imagine now that you want to make more money than 3,300 what can you do you notice something you tell the bank hey all you're telling me is that if you keep my money for one year you'll give me 10% of whatever you have kept right so all I'm gonna do is after a year I'm gonna withdraw my money give me back my money so they have to give you and you say okay that's how much how much should you give me you have to give me thousand one hundred rupees right thank you very much now then you say I'm just gonna do this this one looks way too bad to keep to be kept over here thousand one hundred yeah there it is so now I'm going to put this money back into your bank and the bank may get a little confused but all you're doing is saying that give me back my money and you're putting it back you have all the rights to do that so what does that do do it change is something very important it changes the principle for the next year so thousand is not the principle for the next year you say it is thousand one hundred so thousand one hundred is the principle for calculating the interest for your number two so it's not going to be hundred but ten percent of thousand one hundred so hundred goes something more than hundred is going to come because your principle is increased ten percent of the principle is also increase now luckily it's 10 percent so super easy to calculate it's just dividing this by 10 so it's hundred and ten rupees so you've already made ten rupees more than what you did last year so you're number one nothing changed you made the same hundred by this method but in your number - you made ten rupees more now of course you'll do this again right you'll say wait wait I'm going to take this money back out again give me back my money that's gonna be thousand two hundred and ten rupees now so your thousand two hundred and ten rupees with you and you say I'm going to put this back in again and the bank goes okay something's up earlier so you going to give them say the thousand two hundred 10 is your new principal I think you can see where this is going you're after your if you take money out and put it back in you have a better deal because your principal keeps increasing over here your principal just remains the same so what's the interest gonna be this time it's going to be 10% of thousand two hundred and ten which is one to anyone to piece you're beginning to make bigger profits last time you made a 10 rupee profit this time you're making 11 to be profit on top of this so overall if you notice over this hundred you made 21 rupees more just in the third year so how much is this gonna be thousand three hundred thousand three thousand three hundred and thirty one thousand three hundred and thirty-one now let's update it we have used some cleverness to make some money we should celebrate now if you do this where you take the money out and deposit back in again or rather if the bank says hey I know you can do this I just imagine you did it I just imagine that you took it out and put it back in if the bank makes you this deal then it's called compound interest now you may say that all of this hard work to make thirty one two peas more does not seem that worth it but imagine if this number had been bigger let's say it was a lakh that's that's a that's a hundred times more than a thousand that's a hundred times a thousand so this difference over here which is 31 will also be a hundred times which is basically three thousand one hundred rupees now that's large even more beautiful is when the number of years that you do this for the number of years you keep the money in the bank as that increases this difference just skyrockets now notice that component list is nothing new now when you're given a problem in compound interest you can use that formula that's there but I mean I personally find it much easier to just observe what's happening and notice that this is nothing new this is just percentage increase look at this this thousand you increase it by ten percent you get the principal for the next year ten percent again on this principle you get this new number thousand two hundred and ten increase that by ten percent you eight thousand three hundred and thirty one so it's nothing new and component wrist all you're doing is increasing a number by a given percentage again and again you do it for four years five years you keep doing it that's all component really is so if you understand percentage increase if you know how to increase a number by a given percentage and if you understand how to do it again and again you're done you don't need to know anything else new to do component is problems one small detail here is that this compounding rate we're doing it every year it doesn't have to be a real when it's a year we call it say that this is compounded annually because you're adding the interest back every year if you do it every six months in other words if you find the interest for six months and then you add it to the principal just at six months then it's called compounding half yearly if you do it every year three months it's called doing it quarterly and India many of the banks do it quarterly so if you put money into the bank if you deposit money it's almost always compound interest that you will get I don't know if there are cases where you put money in a bank and you get simple interest so it's good in one way you'll make more money but if you do take a loan it's important to check whether it's simple interest or compound interest because you'll actually end up paying much more money if it's combined interest and you should also particularly look at the frequency of compounding how often are they compounding because sometimes it's not very clear like you may think that they're compounding it yearly or monthly or something but but some some of these people actually compound very quickly especially credit cards for example like some of them have seen compound every day so if you miss one payment the interest you pay on the interest can get much higher than you expect and you may not even notice it even before you notice it the amounts much bigger