At what rate compound interest per annum will 5000 amount to 5618 in 2 years?

DIRECTIONS: Each of the questions given below consists of 2 statements, number I and II respectively. Please read the questions carefully and decide which of the statement (s) is / are necessary to answer the questions.Find the time.Statement I: Amount = Rs. 5618Statement II: Principal = Rs. 5000, Rate = 12% per annum compound interest, compound semi- annually.

1. The data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.
3.  Either statement I or statement II alone is sufficient to answer the question.
4. The data in both the statements I and II is not sufficient to answer the questions.
5. The data in both the statement I and II together is necessary to answer.

Answer (Detailed Solution Below)

Option 5 : The data in both the statement I and II together is necessary to answer.

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Statement I

Amount = Rs. 5618

From the given information we cannot find the time

Statement II

Principal = Rs. 5,000, Rate, r = 12 % per annum , Amount, A = Rs. 5,618

Amount = Principal [1 + (r / 100)]t

Rate = 12 / 2 ⇒ 6 % per annum

5,618 = 5,000 [1 + (6 / 100)]t

⇒ (5,618 / 5000) = (106 / 100)t

⇒ (53 / 50)2 = (53 / 50)t

⇒ 2 = t

As it is compounded semi – annually. So, t = 4 years (i.e. 2 × 2)

So by combining both the equations we can find the time.

∴ The data in both the statement I and II together is necessary to answer

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Solution : Let the compound inteest be r% . <br> `:.` The amount of Rs. 5000 in 2 years `=Rs. 5000xx(1+r/100)^(2)` <br> As per question `5000xx(1+r/100)^(2)=5832` <br> or `(1+r/100)^(2)=5832/5000` <br>or `(1+r/100)^(2)=726/625` <br> or `(1+r/100)^(2)=(27/25)^(2)` <br> or `1+r/100=27/25` [ by taking square root of both of the sides] <br> or `r/100=27/25-1` ltbgt or `r/100=2/25` or `r=(2xx100)/25=8` <br> Hence the rate of compound interest is 8% per annum.

Book: RS Aggarwal - Mathematics

Chapter: 11. Compound Interest

Subject: Maths - Class 8th

Q. No. 8 of CCE Test Paper-11

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8

At what rate per cent per annum will 5000 amount to Rs. 5832 in 2 years, compounded annually?

Present value, P = Rs.5000

Amount, A = Rs.5832

Time, n = 2 years

Now,

Amount (A) = P (1 + R/100)n [Where, A = Amount with compound interest

P = Present value

R = Annual interest rate

n = Time in years]

∴ Amount (A) = P (1 + R/100)n

⇒ 5832 = 5000 (1 + R/100)2

⇒ (1 + R/100)2 = 5832/5000

⇒ (1 + R/100)2 = 2916/2500

⇒ (1 + R/100)2 = (54/50)2

⇒ 1 + R/100 = 54/50

⇒ R/100 = (54/50) - 1

⇒ R/100 = (54 – 50)/50

⇒ R/100 = 4/50

⇒ R = 400/50

⇒ R = 8

∴ Rate = 8 %.

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