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A sum of money doubles itself in 5 years. In how many years will it become fourfold (if interest is compounded)?
- a)15
- b)10
- c)20
- d)12
Correct answer is option 'B'. Can you explain this answer?
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A sum of money doubles itself in 5 years. In how many years will it b...
⇒ 4 = [21/5]T
⇒ 22 = 2T/5
⇒ T/5 = 2
∴ T = 10 yrs.
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A sum of money doubles itself in 5 years. In how many years will it b...
Solution:
Let the sum of money be P.
According to the question, P doubles itself in 5 years, i.e.,
P x (1 + r/100)^5 = 2P
Simplifying the above equation, we get:
(1 + r/100)^5 = 2
Taking the natural logarithm of both sides, we get:
ln(1 + r/100)^5 = ln2
5 ln(1 + r/100) = ln2
ln(1 + r/100) = ln2/5
Now, using the formula for the compound interest, we can find the time taken for the sum of money to become fourfold.
Let the time taken be t years.
Then,
P x (1 + r/100)^t = 4P
Simplifying the above equation, we get:
(1 + r/100)^t = 4
Taking the natural logarithm of both sides, we get:
ln(1 + r/100)^t = ln4
t ln(1 + r/100) = ln4
Substituting the value of ln(1 + r/100) from the earlier equation, we get:
t ln2/5 = ln4
t = ln4 / ln2/5
t = 10 years
Therefore, the sum of money will become fourfold in 10 years if the interest is compounded.
Hence, the correct answer is option 'B'.
Let the sum of money be P.
According to the question, P doubles itself in 5 years, i.e.,
P x (1 + r/100)^5 = 2P
Simplifying the above equation, we get:
(1 + r/100)^5 = 2
Taking the natural logarithm of both sides, we get:
ln(1 + r/100)^5 = ln2
5 ln(1 + r/100) = ln2
ln(1 + r/100) = ln2/5
Now, using the formula for the compound interest, we can find the time taken for the sum of money to become fourfold.
Let the time taken be t years.
Then,
P x (1 + r/100)^t = 4P
Simplifying the above equation, we get:
(1 + r/100)^t = 4
Taking the natural logarithm of both sides, we get:
ln(1 + r/100)^t = ln4
t ln(1 + r/100) = ln4
Substituting the value of ln(1 + r/100) from the earlier equation, we get:
t ln2/5 = ln4
t = ln4 / ln2/5
t = 10 years
Therefore, the sum of money will become fourfold in 10 years if the interest is compounded.
Hence, the correct answer is option 'B'.
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A sum of money doubles itself in 5 years. In how many years will it become fourfold (if interest is compounded)?a)15b)10c)20d)12Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A sum of money doubles itself in 5 years. In how many years will it become fourfold (if interest is compounded)?a)15b)10c)20d)12Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money doubles itself in 5 years. In how many years will it become fourfold (if interest is compounded)?a)15b)10c)20d)12Correct answer is option 'B'. Can you explain this answer?.
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