What is the compound interest on a sum of rupees 12000?

Question 40 Compound Interest Exercise 14.2

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Answer:

Given details are,

Principal = Rs 12000

Amount = Rs 13230

Rate = 5% per annum

Let time = T years

By using the formula,

A = P (1 + R/100)^n

13230 = 12000 (1 + 5/100)^T

13230 = 12000 (105/100)^T

(21/20)^T = 13230/12000\

(21/20)^T = 441/400

(21/20)^T = (21/20)^2

So on comparing both the sides, n = T = 2

∴ Time required is 2years

Video transcript

"hello students welcome to lido's question and answer classroom my name is shaista perozi class and today we are going to find out the value of n that is time yes so let's quickly start with the question what the question says ishira invested a sum of rupees 12 000. so you can clearly understand the sum of 12 000 which is the principal amount at five percent per annum which is our rate of interest and we have to she received an amount of rupees 13 230 which is an amount it is clearly specified that this is the amount which is given after n years so we don't know the time period that is we have considered this as n years so here you have to find out the value of n that is the time period so let's quickly jot down whatever information or details are given to us so it says that the principal is equals to rupees twelve thousand [Music] then rate of interest is five percent amount given to us is rupees 13 230 you have to find out n okay so here n as you know that this is nothing but time so let's quickly take the formula for amount which is already given to us the value of amount is already given so let's quickly write down the formula for amount so my amount is equals to principal that is p 1 plus r that is rate of interest upon 100 raised to n that is the time period so as you know that the amount is 13 230 i am going to write instead of amount 13 [Music] 230 which is equals to principal that is 12 000. one plus rate of interest which is 5 [Music] upon 100 raised to n that is time period which we have to find out so we are going to just solve the brackets part first so i got 13 230 is equals to 12 000 and after solving the l sims as you can see you have to take the l over here i am going to get 105 upon 100 raised to n so now i am quickly taking this 12 000 to the left hand side so i will get this into division which is equal to 105 upon 100 raised to n now what we are going to do is we are going to simplify both the sides so here you can see that 105 divided by 100 will be divisible by 5 so i am going to simplify by dividing 5 and similarly i am going to simplify here also so let's simplify both the size so on division and simplifying i am going to get on left hand side as 441 upon 400 and here i am going to get 21 upon 20 that is i have divided by 5 now as you can clearly see that since i am comparing this 441 upon 421 upon 20 you can clearly see on the left hand side that 441 is nothing but 21 square and 400 is nothing but 220 square so while on comparing left hand side and right hand side you can understand that it's nothing but n which is equals to two years okay so n is equals to two that means our time is equals to two so here you can understand from here that n is nothing but equals to my n is equals to t that is time which is equals to two years okay so we have got down got our answer that is time is equals to two years all right we have received our answer that's all for today uh subscribe to leo for more updates and do comment don't forget to comments like hope you have all understood see you all next time bye take care "

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Answer

Hint: The amount 12,000 doubles which means it becomes $ 2 \times 12,000 = 24,000 $ after 5 years. This means that when the principal amount is Rs.12,000 and the time period is 5 years, the final amount will be Rs. 24,000. So from this we can calculate the interest rate by using the below formula. With the obtained interest rate, the principal amount Rs.12,000 and the time period 20 years, find the final amount at the end of 20th year. Compound interest A is calculated by $ A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T} $ , where P is the principal amount, T is the time period and R is the interest rate.

Complete step-by-step answer:

So, the correct answer is “Rs. 1,92,000”.

Note: The interest can be either simple or compound. In simple interest, the interest amount does not change till the end of the return period whereas in compound interest, the interest amount gradually changes as the interest is imposed on the principal amount plus the previous accumulated interest combined. Compound interest is much greater than Simple interest.

SSC CGL 2022 Tier I Prelims Exam Date Out on the official website of SSC on 31st October 2022! The prelims exam will be conducted from 1st to 13th December 2022. Earlier, SSC CGL Results for Tier II 2021 Marks Status Link has been activated. Candidates can check their marks by visiting the official website. The SSC CGL 2022 is ongoing and the candidates had applied for the same till 13th October 2022. The SSC CGL 2022 Notification was out on 17th September 2022. The SSC CGL Eligibility is a bachelor’s degree in the concerned discipline. This year, SSC has completely changed the exam pattern and for the same, the candidates must refer to SSC CGL New Exam Pattern.