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In how many months will Rs. 8,000 yield Rs. 2,648 as compound interest at 20% per annum compounded semi-annually?
- a)18
- b)24
- c)12
- d)30
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
In how many months will Rs. 8,000 yield Rs. 2,648 as compound interest...
Let n be number of half years
Amount = 8000 + 2648 = 10648
From the problem statement
⇒ 10648 = 8000(1 + 0.2/2)n
⇒ 1.331 = (1.1)n
⇒ n = 3
∴ 3 half year means 18 months.
Amount = 8000 + 2648 = 10648
From the problem statement
⇒ 10648 = 8000(1 + 0.2/2)n
⇒ 1.331 = (1.1)n
⇒ n = 3
∴ 3 half year means 18 months.
Most Upvoted Answer
In how many months will Rs. 8,000 yield Rs. 2,648 as compound interest...
Calculation of Time taken to yield compound interest:
- Given Principal (P) = Rs. 8,000
- Amount (A) = P + Compound Interest (CI) = Rs. 8,000 + Rs. 2,648 = Rs. 10,648
- Rate of interest (R) = 20% per annum compounded semi-annually
- Time period (n) = Number of months
Formula for Compound Interest:
- A = P(1 + R/100)^n
- 10,648 = 8,000(1 + 0.2/2)^(2n)
- 10,648/8,000 = (1.1)^2n
- 1.331 = 1.1^(2n)
Calculating the time period:
- Taking log on both sides: log(1.331) = log(1.1^(2n))
- log(1.331) = 2n * log(1.1)
- n = log(1.331) / (2 * log(1.1))
- n = 0.1239 / 0.0414
- n = 2.99
Therefore, the time taken to yield Rs. 2,648 as compound interest at 20% per annum compounded semi-annually is approximately 3 months.
Therefore, the correct answer is option 'A' - 18 months.
- Given Principal (P) = Rs. 8,000
- Amount (A) = P + Compound Interest (CI) = Rs. 8,000 + Rs. 2,648 = Rs. 10,648
- Rate of interest (R) = 20% per annum compounded semi-annually
- Time period (n) = Number of months
Formula for Compound Interest:
- A = P(1 + R/100)^n
- 10,648 = 8,000(1 + 0.2/2)^(2n)
- 10,648/8,000 = (1.1)^2n
- 1.331 = 1.1^(2n)
Calculating the time period:
- Taking log on both sides: log(1.331) = log(1.1^(2n))
- log(1.331) = 2n * log(1.1)
- n = log(1.331) / (2 * log(1.1))
- n = 0.1239 / 0.0414
- n = 2.99
Therefore, the time taken to yield Rs. 2,648 as compound interest at 20% per annum compounded semi-annually is approximately 3 months.
Therefore, the correct answer is option 'A' - 18 months.
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