At what rate of compound interest per annum will 20000 amount to 26620 in 3 years

Solution

The correct option is BRs 6,620A=P×[1+r100]n, where P is the principal, r is the rate of interest and n is the time period. C.I = A - P Here, P = ₹ 20,000, r = 10 %, and n = 3 yearsA=20,000×[1+10100]3 A=20,000×[11×11×1110×10×10] A = ₹ 26,620So, C.I = 26,620 - 20,000 = ₹ 6,620

Solution : Here, Principal amount `(P) = 20000` Rs<br> So, amount after first year ` = 20000(1+10/100)^1`<br> Amount after second year ` = 20000(1+10/100)(1+10/100)^1`<br> Amount after third year ` = 20000(1+10/100)(1+10/100)(1+12/100)^1`<br> ` = 20000**11/10**11/10**112/100 = 224**121 = 27104` Rs<br> `:.` Compound interest ` = 27104-20000 = 7104` Rs<br>

Video Transcript

got this problem there was some of money and we've invested it and at three years that amount Is 26,620. And at four years it's grown 29-82 and were asked what the interest rate is that were getting And what was the original sum of money? Other words original amount? Well this compounds which means the balance be at time. T is simply initial amount times one plus are to the t the rate here the interest rate that we're looking for. So this is the interest rate we're looking for. So we know it three years the balance be at three It's 26 6 20 And that's equal to the original balance times one plus R. To the third. Then we know b. a. four It's 29-82 which is the original valentine's one plus R To the 4th, Don't We? All right. So if I take B A four divided by B. Of three. Well That means I have 29-82 Divided by 26 6 20. And that's B 01 plus R. To the fourth over B 01 plus R cubed might be zeroes, cancel out one plus R to the third. Takes out one of those. So this ratio right here that I get well tell me one plus R. Won't it? Okay. So if I take 29 to 82 divided by 26 6 20 then I get I get 1.1 equals one plus R. Therefore our is 0.1 and as a percent That's 10%. Because I move the decimal to places. Right? Okay, so there's my interest rate 10%. And now to get the B0. Well Let's look at what B three is 26 6 20 is B zero. The initial balance one plus 0.1 to the third. So this is 26 620 Is equal to, well 1.1 to the third Is 1.331 times B0. So now divide by 1.331 on both sides. And we get 20,000 is initial balance. So our initial some It was 20,000 What we started with.

What is the sum (in Rs.) of money which will become Rs. 26620 at the rate of 10% per annum at compound interest in three years?

This question was previously asked in

SSC MTS Previous Year Paper 76 (Held On : 25-Oct-2017 Shift 3)

View all SSC MTS Papers >

1. 20000
2. 22000
3. 25000
4. 26000

Answer (Detailed Solution Below)

Option 1 : 20000

Free

Noun & Pronoun: Fill In The Blanks (Most Important Rules)

15 Questions 15 Marks 12 Mins

Let the sum of money be s.

Amount = P [(1 + r/100)t

Where, P = Principal, r = rate of interest, and t = time period

The amount after 3 years: P [(1 + r/100) t = P(1 + 0.1)3 = P × 1.13 = 1.331P = 26620

⇒ P = 26620/1.331 = Rs. 20000

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