JEE Exam > JEE Questions > A sum of money doubles itself in 5 years. In...
Start Learning for Free
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?
Verified Answer
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.
Most Upvoted Answer
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'.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
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?
Question Description
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 2025 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 2025 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?.
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 2025 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 2025 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?.
Solutions 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? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of 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? defined & explained in the simplest way possible. Besides giving the explanation of
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?, a detailed solution 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? has been provided alongside types of 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? theory, EduRev gives you an
ample number of questions to practice 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? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup