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A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.?
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A sum of money doubles itself in 4 years at S.I. In how many years wil...
Understanding Simple Interest (S.I.)
To solve the problem of how long it takes for money to amount to 8 times itself under Simple Interest (S.I.), we first need to comprehend the relationship between time, interest, and the principal amount.
Doubling Time
- A sum doubles itself in 4 years at S.I.
- This implies that the interest earned in 4 years equals the principal amount (P).
Formula:
Total Amount (A) = Principal (P) + Interest (I)
- Therefore, after 4 years:
A = P + P = 2P
Finding the Rate of Interest
- The interest (I) for 4 years can be expressed as:
I = P * r * t
where r is the rate and t is time in years.
- Since we know I = P, we can set up the equation:
P = P * r * 4
- Simplifying gives:
r = 1/4 or 25% per annum.
Calculating Time for 8 Times
- Now, to find out when the amount becomes 8 times itself:
A = 8P
- The interest (I) in this case would be:
I = A - P = 8P - P = 7P
- Using the interest formula again:
7P = P * r * t
7 = r * t
- Substituting r = 1/4 into the equation:
7 = (1/4) * t
- Therefore, solving for t gives:
t = 28 years.
Conclusion
In conclusion, it will take 28 years for a sum of money to amount to 8 times itself at a rate of 25% per annum under Simple Interest.
To solve the problem of how long it takes for money to amount to 8 times itself under Simple Interest (S.I.), we first need to comprehend the relationship between time, interest, and the principal amount.
Doubling Time
- A sum doubles itself in 4 years at S.I.
- This implies that the interest earned in 4 years equals the principal amount (P).
Formula:
Total Amount (A) = Principal (P) + Interest (I)
- Therefore, after 4 years:
A = P + P = 2P
Finding the Rate of Interest
- The interest (I) for 4 years can be expressed as:
I = P * r * t
where r is the rate and t is time in years.
- Since we know I = P, we can set up the equation:
P = P * r * 4
- Simplifying gives:
r = 1/4 or 25% per annum.
Calculating Time for 8 Times
- Now, to find out when the amount becomes 8 times itself:
A = 8P
- The interest (I) in this case would be:
I = A - P = 8P - P = 7P
- Using the interest formula again:
7P = P * r * t
7 = r * t
- Substituting r = 1/4 into the equation:
7 = (1/4) * t
- Therefore, solving for t gives:
t = 28 years.
Conclusion
In conclusion, it will take 28 years for a sum of money to amount to 8 times itself at a rate of 25% per annum under Simple Interest.
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A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.?
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A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.?.
A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of money doubles itself in 4 years at S.I. In how many years will it amount to 8 times itself.?.
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