The difference between simple and compound interest on the same sum of money at 6 2/3

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• Compound Interest Exercise 14.1
• Compound Interest Exercise 14.2
• Compound Interest Exercise 14.3
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• Compound Interest Exercise 14.5

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RD Sharma Solutions Class 8 Mathematics Solutions for Compound Interest Exercise 14.2 in Chapter 14 - Compound Interest

Question 37 Compound Interest Exercise 14.2

The difference in simple interest and compound interest on a certain sum ofmoney at 6 2/3 % per annum for 3 years in Rs. 46. Determine the sum.

Answer:

Given,

Time = 3 years

Rate = 6 2/3 % per annum = 20/3%

Let principal = Rs P

Compound Interest (CI) – Simple Interest (SI) = Rs 46

C.I – S.I = Rs 46

By using the formula,

P [(1 + R/100)^n - 1] - (PTR)/100 = 46

P [(1 + 20/3×100)^3 - 1] - (P(3)(20/3))/100 = 46

P[(1 + 20/300)^3 – 1] - P/5 = 46

P[721/3375] - P/5 = 46

721/3375P - 1/5P = 46

(721P-675P)/3375 = 46

46P = 46 × 3375

46P = 46 × 3375/46

= 3375

∴ The sum is Rs 3375

Video transcript

"hello students welcome to rito's question and answer classroom my name is shaista ferozi class and today we are going to find out some interesting concepts okay so here we are going to find out the diff sum okay as you can see that you are going to find out the sum so let's first read what the question says the question says the difference in simple interest and compound interest on a certain sum of money at six two by three percent per annum for three years is rupees 46 determine the sum now you can clearly understand from the question that this difference of simple interest and compound interest is rupees 46 which is given also we have given the rate of interest is six two by three per annum and the time period as you can see it is for three years okay so we are just going to quickly jot down whatever details which are being given over here first of all i'll write down the difference which is given as compound interest minus simple interest which is equals to rupees 46 also you can see the rate of interest is given as 6 2 upon 3 percent per annum now since you can see that this is the mixed fraction i have to convert it into improper fraction which will be 20 upon 3 also time is given so time is three years okay now let's say we will suppose that our principle be because the principle is not given and we want the principle so we will just say let principle be p okay so let's quickly start our question the solution for this okay we will start with whatever is given to us and we have been given that compound interest is equals compound interest minus simple interest is equals to rupees 46. i am going to just write down the formula of compound interest and simple interest over here so the compound interest formula is p 1 plus r upon 100 raised to n minus 1 minus simple interest formula is p into time that is t into rate of interest upon 100 which is equal to 46 so i'm just going to copy down 46 now we are going to substitute the value since we don't know the sum or we don't know the principal amount i am just going to write down p then i am going to write down 1 plus r since my rate of input is 20 upon 3 i am going to write down 3 and the 100 which was in the question raised to n that is the period of time which is 3 years minus 1 minus i am going to substitute the values of time that is 3 rate of interest that is 20 upon 3 and the 100 which is in the question formula is equals to 46 now i am going to solve the bracket by taking an lcm of this which you can see first i will write down the multiplication part as 20 and 3 upon 100 is nothing but 300 raised to 3 minus 1 minus p and after the solution after solving this whole bracket okay the things which are going to cancel over here we will just cancel it like three three gets cancelled and twenty five za is hundred so i'm going to get p upon five which is equals to forty six okay now we are going to solve this whole bracket by taking an lcm and on taking analysis lcm and adding whatever is given we are going to get p 320 upon 300 raised to 3 minus 1 minus p upon 5 is equals to 46 now we are just going to do the solution for this whole thing okay so i'm just going to solve this since it's the 320 upon 30 cube okay so i'm just taking the cube of this and on solving this whole thing i am going to get as p into 7 21 upon 3 3 7 5 that is 3775 minus p upon 5 is equals to 46 okay so i've taken the cube i have uh taken the lcm also through the one because after multiplying this and then taking the lcm with one i am going to get t into 721 upon 375 so once i get this again i will have to take an lcm of this whole thing okay that is you have 303 375 in the denominator and 5 is the denominator so i'm just going to convert this and you will get 721 p minus 675 p upon 3375 which is equals to 46 okay so after subtracting this i am going to get 46 p upon 3375 which is equals to 46 and therefore p will be equals to 46 multiplied by 3370 after the transposition of the numbers from right hand side to the left hand side okay and then after solving this i am going to get t is equal to 3 375 rupees okay so this is my principal amount as you can see that we have got 3375 as our sum which is our principal amount okay so hope you have all understood alright that's all for today see you next time bye bye take care "

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