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In what time will a sum of money double itself @ 20% per annum (p.a.) simple interest?
- a)10 years
- b)5 years
- c)2 years
- d)4 years
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In what time will a sum of money double itself @ 20% per annum (p.a.) ...
Solution:
Let the sum of money be x.
Simple Interest (SI) = (P * R * T)/100
where P is the principal, R is the rate of interest, and T is the time period.
Given, R = 20% p.a.
We need to find the time period (T) in which the sum of money will double itself.
We know that the amount after T years with simple interest is given by:
Amount = P + SI
For doubling the principal amount, the amount should be equal to 2P.
Therefore, we can write the equation as:
2x = x + (x * 20 * T)/100
=> 2x = x + 0.2xT
=> 0.8x = 0.2xT
=> T = (0.8x/0.2x) years
=> T = 4 years
Therefore, the sum of money will double itself in 4 years at a rate of 20% per annum simple interest.
Hence, option (d) is the correct answer.
Let the sum of money be x.
Simple Interest (SI) = (P * R * T)/100
where P is the principal, R is the rate of interest, and T is the time period.
Given, R = 20% p.a.
We need to find the time period (T) in which the sum of money will double itself.
We know that the amount after T years with simple interest is given by:
Amount = P + SI
For doubling the principal amount, the amount should be equal to 2P.
Therefore, we can write the equation as:
2x = x + (x * 20 * T)/100
=> 2x = x + 0.2xT
=> 0.8x = 0.2xT
=> T = (0.8x/0.2x) years
=> T = 4 years
Therefore, the sum of money will double itself in 4 years at a rate of 20% per annum simple interest.
Hence, option (d) is the correct answer.
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