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?
- Rs. 2,500
- Rs. 2,480
- Rs. 2,560
- Rs. 2,520
Answer (Detailed Solution Below)
Option 3 : Rs. 2,560
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CT : General Intelligence and Reasoning (Practice Set)
10 Questions 20 Marks 8 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 28, 2022
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What sum of money will amount to Rs. 9,261 in 3 years @ 5 % per annum compound interest?
Question
A
Rs. 6,000
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B
Rs. 9,000
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C
Rs. 8,000
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D
Rs. 8,800
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E
Rs. 4,000
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Solution
The correct option is E
Rs. 8,000
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