In what time will 8000 amount to 9261 at 10% per annum interest compounded half yearly?

A sum of Rs. 8,000 invested at 10% p.a. amounts to Rs. 9,261 in a certain time, interest compounded half–yearly. What will be the compound interest (in Rs) on the same sum for the same time at double the earlier rate of interest, when interest is compounded annually?

1. Rs. 2,500
2. Rs. 2,480
3. Rs. 2,560
4. Rs. 2,520

Answer (Detailed Solution Below)

Option 3 : Rs. 2,560

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SSC CGL 2021 Tier-I (Held On : 11 April 2022 Shift 1)

100 Questions 200 Marks 60 Mins

Given:

P = 8000, A = 9261 and r = 10%

If interest compounded half–yearly, then = 10/2 = 5%

As we know,

A = P (1 + r/100)t

⇒ 9261 = 8000 (1 + 5/100)t

⇒ (1 + 1/20 )t = 9261/8000

⇒ (21/20)t = (21/20)3

⇒ t = 3 years

As given, interest compounded half–yearly, then

Time = 3/2 years [1 year and 6 month]

Now,

P = 8000, r = 10 × 2 = 20% and t = 3/2

As we know,

A = P (1 + r/100)t

A = 8000 (1 + 20/100) × (1 + 10/100)

⇒ A = 8000 × 120/100 × 110/100

⇒ A = 10560

CI = 10560 – 8000 = 2560

As we know,

P : A for 1 year = ∛8000 : ∛9261 = 20 : 21

Percentage = 1/20 × 100 = 5% (satisfied)

Time = 1 year 6 month

Now, rate = 20%

Rate for 1 year 6 month = 20 + 10 + (20 × 10)/100 = 30 + 2 = 32%

⇒ 32% of 8000

⇒ 2560

Last updated on Oct 21, 2022

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Q. In what time 8000 Rs. will amount to 9261 Rs. at 10% per annum compound interest, when the interest is compounded half yearly?
Answer: [A] 1.5 years
Notes: Interest is compounded half yearly. ∴ Rate of interest = 5% $ Time = \frac{n}{2}\ years$ $ \because A = P(1 + \frac{R}{100})^{T}$ $ => 9261 = 8000 (1 + \frac{5}{100})^{n}$ $ => \frac{9261}{8000} = (\frac{21}{20})^{n}$ $ => (\frac{21}{20})^{3} = (\frac{21}{20})^{n}$ $ => n = 3\ half\ years$ $ = \frac{3}{2}\ years = 1\frac{1}{2}\ years$ Hence option [A] is correct answer.

Correct Option: B

Interest is compounded half yearly.
Given that , P = ₹ 8000 , A = ₹ 9261 , Rate of interest = 5%

Using the given formula ,

A = P		1 +	R		T
100

⇒  9261 = 8000		1 +	5		n
100

⇒	9261	=		21		n
8000	20

⇒		21		3	=		21		n
20		20

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