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A sum of amount at r% compound interest doubles in 3 years. In 9 years it will be k times of the original principal. What is the value of k?
- a)10
- b)9
- c)6
- d)8
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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A sum of amount at r% compound interest doubles in 3 years. In 9 years...
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A sum of amount at r% compound interest doubles in 3 years. In 9 years...
Given data:
Amount at r% CI doubles in 3 years.
So, the CI earned annually will be r/100.
Using the formula for CI:
Amount = P(1 + r/100)^n
2P = P(1 + r/100)^3
(1 + r/100)^3 = 2
1 + r/100 = ∛2
r/100 = (∛2 - 1)
r = 100(∛2 - 1)
Now, we need to find the value of k when the amount will be k times of the original principal in 9 years.
Using the formula for CI:
Amount = P(1 + r/100)^n
Amount = P(1 + (∛2 - 1))^9
Amount = P(∛2)^9
Amount = 2.828P
So, the amount after 9 years will be 2.828 times the original principal.
Therefore, the value of k will be 2.828/1 = 8.
Hence, the correct answer is option D (8).
Amount at r% CI doubles in 3 years.
So, the CI earned annually will be r/100.
Using the formula for CI:
Amount = P(1 + r/100)^n
2P = P(1 + r/100)^3
(1 + r/100)^3 = 2
1 + r/100 = ∛2
r/100 = (∛2 - 1)
r = 100(∛2 - 1)
Now, we need to find the value of k when the amount will be k times of the original principal in 9 years.
Using the formula for CI:
Amount = P(1 + r/100)^n
Amount = P(1 + (∛2 - 1))^9
Amount = P(∛2)^9
Amount = 2.828P
So, the amount after 9 years will be 2.828 times the original principal.
Therefore, the value of k will be 2.828/1 = 8.
Hence, the correct answer is option D (8).
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