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

Question 2 Compound Interest Exercise 14.2

Find the principal if the interest compounded annually at the rate of 10% for twoyears is Rs. 210.


Given details are,

Rate = 10 % per annum

Compound Interest (CI) = Rs 210

Time (t) = 2 years

By using the formula,

Let P be ‘x’

CI = A – P

210 = P (1 + R/100) n – P

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

= x [(1 + 10/100)2 – 1]

= x [(110/100)2 – 1]

210 = x ((1.1)2 – 1)

x = 210 / ((1.1)2 – 1)

= 210/0.21

= Rs 1000

∴ The required sum is Rs 1000

Video transcript
"hello students welcome to lido's question and answer classroom my name is shaisa firozi class and today we are going to find out the principle so let's focus at the question what the question says the question says find the principle so as i told you you have to find out the principle or the sum if the interest compounded annually at a rate of 10 percent so my rate is 10 percent for two years that is the time period is two years and since it says interest is rupees 210 so whatever details are given let's quickly jot down it so as you can see that my rate of interest is rupees sorry is 10 percent and the time is for two years then my compound interest is rupees 210 okay and i since i don't have the principle i'll just suppose let principle be x okay so i'm taking my principle as x rupees this is what we have to find out so let's quickly write down the formula for this okay so let's say compound interest since you know that our compound interest is equals to amount minus principle okay because we have been given the compound interest which is 210 rupees i'm going to take compound interest is equal to amount minus principle now as you can see we don't have the amount also with us so we don't have amount we don't have principle we have compound interest so we are going to take the amount formula in this so that amount goes out so let us take the formula compound interest is 210 my amount formula which is t 1 plus r upon 100 raised to n minus p okay now i am going to substitute the values which are given so my compound increase this sorry my compound interest is 210 my principal i don't know i'm writing it as x because i have supposed it as x then 1 plus my rate of interest is 10 upon 100 my time period which is n is two years minus prince one okay so now i am going to solve the bracket part so 210 is equal to x now since once once more you have to consider this this whole part you have to take an lcm and by taking lcm i am going to get 110 upon 100 raised to 2 minus 1 now i am going to take the square of these okay i am going to solve this bracket by taking the square so after solving this whole part of the bracket i am going to get 210 x into 1.1 square minus 1 so now i am going to take x on one side and all other numbers on one side by transposing it so i'm get going to get 210 upon 1.1 square raise to minus 1 once again i'm going to take an lcm of this whole part after solving 1.1 and taking an l same with 1 i am going to get x is equals to 210 upon 0.21 okay so since i got this now what i am going to do is i am going to divide this and therefore i will get on division of on division of 210 upon 0.21 i am going to get my value as x is rupees 1000 okay so my x is rupees thousand and what is my x my x is the principle so yes so therefore i am going to write down as my principle or you can say my sum is nothing but equals to rupees thousand so that's what my answer is all guys that's all for today see you all next time take care bye"
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