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At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually?
Most Upvoted Answer
At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 1...
Understanding the Problem
To find the rate percent per annum for a sum of Rs. 12000 to amount to Rs. 15972 in three years with compound interest, we can use the compound interest formula.
Compound Interest Formula
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
- A = Amount after time t
- P = Principal amount (initial sum)
- r = Rate of interest (decimal)
- n = Number of times interest is compounded per year
- t = Time in years
Since the interest is compounded annually in this case, n = 1.
Given Values
- P = Rs. 12000
- A = Rs. 15972
- t = 3 years
Steps to Calculate Rate
1. Substituting Known Values:
- Substitute A, P, and t into the formula:
15972 = 12000(1 + r)^3
2. Rearranging the Equation:
- Divide both sides by 12000:
(1 + r)^3 = 15972 / 12000
3. Calculating the Right Side:
- (1 + r)^3 = 1.331
4. Taking the Cube Root:
- 1 + r = (1.331)^(1/3)
5. Calculating r:
- r ≈ 0.1 (after calculation)
- Convert r to percentage: r ≈ 10%
Conclusion
The rate percent per annum at which Rs. 12000 will amount to Rs. 15972 in three years, when compounded annually, is approximately 10%.
To find the rate percent per annum for a sum of Rs. 12000 to amount to Rs. 15972 in three years with compound interest, we can use the compound interest formula.
Compound Interest Formula
The formula for compound interest is:
A = P(1 + r/n)^(nt)
Where:
- A = Amount after time t
- P = Principal amount (initial sum)
- r = Rate of interest (decimal)
- n = Number of times interest is compounded per year
- t = Time in years
Since the interest is compounded annually in this case, n = 1.
Given Values
- P = Rs. 12000
- A = Rs. 15972
- t = 3 years
Steps to Calculate Rate
1. Substituting Known Values:
- Substitute A, P, and t into the formula:
15972 = 12000(1 + r)^3
2. Rearranging the Equation:
- Divide both sides by 12000:
(1 + r)^3 = 15972 / 12000
3. Calculating the Right Side:
- (1 + r)^3 = 1.331
4. Taking the Cube Root:
- 1 + r = (1.331)^(1/3)
5. Calculating r:
- r ≈ 0.1 (after calculation)
- Convert r to percentage: r ≈ 10%
Conclusion
The rate percent per annum at which Rs. 12000 will amount to Rs. 15972 in three years, when compounded annually, is approximately 10%.
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At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually?
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At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually?.
At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for At what rate percent per annum will a sum of Rs. 12000 amount to Rs. 15972 in three years, when the interest is compounded annually?.
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