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The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is
- a)5
- b)4
- c)6
- d)2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The least number of complete years in which a sum of money put out at ...
P [1 + (r/100)]n > 2P
⇒ P [1 + (20/100)]n > 2P
[1 + (2/10) ]n > 2
[12 / 10]n > 2
[6/5]n > 2
{6/5 * 6/5 * 6/5 * 6/5} > 2
∴ n = 4
⇒ P [1 + (20/100)]n > 2P
[1 + (2/10) ]n > 2
[12 / 10]n > 2
[6/5]n > 2
{6/5 * 6/5 * 6/5 * 6/5} > 2
∴ n = 4
Most Upvoted Answer
The least number of complete years in which a sum of money put out at ...
P [1 + (r/100)]n > 2P
⇒ P [1 + (20/100)]n > 2P
[1 + (2/10) ]n > 2
[12 / 10]n > 2
[6/5]n > 2
{6/5 * 6/5 * 6/5 * 6/5} > 2
∴ n = 4
⇒ P [1 + (20/100)]n > 2P
[1 + (2/10) ]n > 2
[12 / 10]n > 2
[6/5]n > 2
{6/5 * 6/5 * 6/5 * 6/5} > 2
∴ n = 4
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The least number of complete years in which a sum of money put out at ...
Solution:
Let the sum of money be P.
After the first year, the amount becomes P(1+20/100)=P(6/5).
After the second year, the amount becomes P(6/5)(6/5)=P(36/25).
Now, we need to find the least number of complete years in which the amount will be more than doubled.
Let's assume it takes n years to double the amount.
So, the amount after n years will be P(6/5)^n > 2P
(6/5)^n > 2
n*log(6/5) > log(2)
n > log(2)/log(6/5)
n > 3.8 (approx.)
Hence, the least number of complete years required to double the amount is 4.
Therefore, option B is the correct answer.
Let the sum of money be P.
After the first year, the amount becomes P(1+20/100)=P(6/5).
After the second year, the amount becomes P(6/5)(6/5)=P(36/25).
Now, we need to find the least number of complete years in which the amount will be more than doubled.
Let's assume it takes n years to double the amount.
So, the amount after n years will be P(6/5)^n > 2P
(6/5)^n > 2
n*log(6/5) > log(2)
n > log(2)/log(6/5)
n > 3.8 (approx.)
Hence, the least number of complete years required to double the amount is 4.
Therefore, option B is the correct answer.
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The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled isa)5b)4c)6d)2Correct answer is option 'B'. Can you explain this answer?
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