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At what rate of interest will a sum of money become 7/5 of itself in 8 years.?
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At what rate of interest will a sum of money become 7/5 of itself in 8...
Understanding the Problem
To determine the rate of interest at which a sum of money becomes 7/5 of itself in 8 years, we can use the formula for compound interest.
Formula for Compound Interest
The formula for calculating the amount (A) after a certain period under compound interest is:
A = P(1 + r)^t
Where:
- A = Final amount
- P = Principal amount
- r = Rate of interest (in decimal)
- t = Time (in years)
Given Values
- Final Amount (A) = 7/5 * P
- Time (t) = 8 years
Setting Up the Equation
We can substitute the known values into the compound interest formula:
7/5 * P = P(1 + r)^8
Solving for the Rate of Interest (r)
1. Cancel P from both sides (assuming P ≠ 0):
7/5 = (1 + r)^8
2. Take the eighth root of both sides:
(1 + r) = (7/5)^(1/8)
3. Solve for r:
r = (7/5)^(1/8) - 1
Calculating the Rate
Using a calculator, we find that (7/5)^(1/8) is approximately 1.0852. Therefore:
- r ≈ 0.0852 or 8.52%
Conclusion
Thus, the rate of interest required for a sum of money to become 7/5 of itself in 8 years is approximately 8.52%.
To determine the rate of interest at which a sum of money becomes 7/5 of itself in 8 years, we can use the formula for compound interest.
Formula for Compound Interest
The formula for calculating the amount (A) after a certain period under compound interest is:
A = P(1 + r)^t
Where:
- A = Final amount
- P = Principal amount
- r = Rate of interest (in decimal)
- t = Time (in years)
Given Values
- Final Amount (A) = 7/5 * P
- Time (t) = 8 years
Setting Up the Equation
We can substitute the known values into the compound interest formula:
7/5 * P = P(1 + r)^8
Solving for the Rate of Interest (r)
1. Cancel P from both sides (assuming P ≠ 0):
7/5 = (1 + r)^8
2. Take the eighth root of both sides:
(1 + r) = (7/5)^(1/8)
3. Solve for r:
r = (7/5)^(1/8) - 1
Calculating the Rate
Using a calculator, we find that (7/5)^(1/8) is approximately 1.0852. Therefore:
- r ≈ 0.0852 or 8.52%
Conclusion
Thus, the rate of interest required for a sum of money to become 7/5 of itself in 8 years is approximately 8.52%.
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At what rate of interest will a sum of money become 7/5 of itself in 8 years.?
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At what rate of interest will a sum of money become 7/5 of itself in 8 years.? 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 At what rate of interest will a sum of money become 7/5 of itself in 8 years.? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate of interest will a sum of money become 7/5 of itself in 8 years.?.
At what rate of interest will a sum of money become 7/5 of itself in 8 years.? 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 At what rate of interest will a sum of money become 7/5 of itself in 8 years.? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate of interest will a sum of money become 7/5 of itself in 8 years.?.
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