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Finding simple interest for many years

Have you wondered why we call simple interest 'simple'? Also, let's understand the basics behind the famous formula for calculating simple interest. Created by Aanand Srinivas.

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Video transcript

you now know how to find the interest when the amount of time you borrowed is only one year but what happens if it's many years so for one year you know that the interest the interest is going to be equal to the rate divided by 100 that's going to give you the amount you should pay for a principal of one rupee multiplied by the principal so that you can find out how much you have to give for the principal amount of rupees now this you already know so let's say that you borrowed 500 from somebody and you borrowed it at a rate of interest of 10% now I want you to take a couple of moments and calculate what the interest will be the principal is 500 the rate is 10 so 500 into 10 by 100 or 500 by 10 which is going to be 50 so right now you've just borrowed it now so 0 years have passed from you borrowing that money and as we go this way more and more years are gonna pass so one year has passed and you know what to do for that you just calculated that the answer would there is gonna be 50 rupees is going to be the interest 50 rupees so how much is the total amount you must pay after one year you must pay the 500 and on top of that you must pay the 50 interest 10% on 500 now what about one more year after that how much how much should you pay if you have not paid them anything you're still waiting with that money then how much would you pay so two years have passed this does not look like two two years have passed now you must pay the 500 anyway that's your principal you have to always pay this money on top of that you had some interest that you had to pay from last year and now again this year for 500 you have to pay another 10% so 10% of 500 another 50 what about next year so you go to 3 years and I think you can see what's gonna happen you're gonna have a 500 which is the original principal the 250 rupees that you have to pay from last year a 50 and another 50 and for this year because three years have passed you've held on to the money of the 500 for one more year so you pay another four so this is how it keeps increasing so to pay more and more money as you hold this 500 rupees that you borrowed the principal that you borrowed now one of the questions you might have is why exactly is this called simple interest it may not seem too simple the reason it's called that is that each year you pay interest of only 50 rupees which is 10% of 500 so you borrow 500 every year you pay interest on that 500 the one that you started with now what is the other way in which you could do it the person who gave you the money can say first year you owed me 500 you paid 50 for that no problem but now you've not given me anything which means this year you owe me 500 50 rupees so I must calculate my interest not assuming you owe me 500 but you owe me 550 and how much will that be so you have to pay me 55 rupees instead of just 50 rupees and then if you're wondering how I calculated this I just did 550 it's a total amount so 10 percent of 55 10 percent of 10 percent of 550 I'm sorry and that's going to be divided by 10 55 that's really not the point your the point is in order that the amount can keep increasing and when you do that when you keep changing the principle that's called compound interest and when you don't do that every year when you calculate for the same original principle then it's called simple interest and we're only gonna care about simple interest right now now if you want to know how to calculate the interest for many years when you know how to calculate for one year the answer is very simple calculate for one year and then multiply by how many ever years you have that's it this this entire video is over but if you want to look at an example to see how this works let's do that let's say that you borrowed six thousand twenty five rupees that's an extremely specific amount of money to borrow so you borrowed six thousand twenty five rupees and you borrowed it at a rate of 10% per annum and you must calculate the rate of interest or the the interest you will pay this is of course the rate of interest the interest that you will pay after not one year but three years three years so the interest after three years now I'm just gonna go up here and make you notice something so you notice that the interest I paid in the first little it's changes back to simple interest yeah it's fifty here for 250 is your 350 is your and notice the pattern in the first year you'll pay 50 second year you'll pay twice that amount third year you'll pay thrice that amount so with this pattern in mind all you have to do is come back here and say oh you want the interest after three years I don't care I'm just going to calculate the interest after one year and multiplied by three so I'm going to forget that this three year question exists and just look at this and I know how to do this I borrowed a sum of six thousand twenty-five which is my principal PRI ncip al and I borrowed at this rate and now I'll have to calculate is my interest for one year and this I know how to do so let me do that I'll just unpack this in my head I'll say okay for 100 rupees if I had for every hundred rupees I borrow I must pay 10 rupees is my interest so for six thousand twenty five rupees that I borrowed how much should I pay as my interest per your so interest and now I know that I can just use the ratio the fact that these two ratios will be equal and I know what I will get my interest will be equal to if I multiply both sides by 10 then I will get six thousand twenty-five divided by ten or six hundred and two point five rupees then the exact number here doesn't really matter so I know this is how much interest I will pay for one year and that's important to notice here that's not the question the question is for three years so I'm going to write interest for one year now all I have to do to calculate my interest for three years the interest for three years is to multiply this by three so you can you can just do that if you want to six to six hundred and two point five into three I'm just going to leave it like this it's thousand eight hundred and seven point five I hope thousand eight hundred and seven point five so now you can notice that it really doesn't matter what the number of yours is whether it's three years four years five years because it's a simple interest all you have to do is calculate the interest for one year and then multiply for how many over years you want and that's it and you already know how to do this really really well so all you will do is you will calculate the interest the interest for one year which what is that that will simply be equal to the rate the rate divided by a hundred multiplied by the principal by the principal PRI ncip al and that's it and why does this work the rate by 100 gives you the interest for one rupee and multiplied by the principle gives you the interest for principle rupees and this is done but all of this is still for only vanya as long as you hold it for one year so now if you move this here if you want it for many years what should you do nothing all you have to do is multiply with the number of years you want in this case if it's three it's three if it's for its for if it's n its n so the interest at the end of n years of holding something will be the rate divided by hundred multiplied by the principal multiplied by the number of years you want and this is the famous or infamous P n R by hundred P and R by hundred or PRT by 100 formula for the interest for the simple interest after n years but you now know exactly why it works