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An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are?
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An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth ye...
Understanding the Problem
To find the principal amount (p) and the rate of interest (r), we know that:
- Amount after 2 years: A2 = Rs. 5100.5
- Amount after 4 years: A4 = Rs. 5203
Using the formula for compound interest, we can express the amounts as follows:
Amount Formulas
- A2 = p(1 + r/100)²
- A4 = p(1 + r/100)⁴
Setting Up the Equations
From the above formulas, we can create two equations:
- Equation 1: p(1 + r/100)² = 5100.5
- Equation 2: p(1 + r/100)⁴ = 5203
Dividing the Equations
To eliminate p, we divide Equation 2 by Equation 1:
- (p(1 + r/100)⁴) / (p(1 + r/100)²) = 5203 / 5100.5
This simplifies to:
- (1 + r/100)² = 5203 / 5100.5
Calculating the Rate
Calculate the right-hand side:
- (1 + r/100)² = 1.01996 (approximately)
Taking the square root gives:
- 1 + r/100 = 1.00995
Thus, r = (1.00995 - 1) * 100 ≈ 0.995%
Finding the Principal
Substituting r back into Equation 1:
- p(1 + 0.00995)² = 5100.5
- p * 1.0199 = 5100.5
Solving for p gives:
- p ≈ 5000
Final Values
- Principal amount, p = Rs. 5000
- Rate of interest, r ≈ 0.995% per annum
This calculation provides both the principal and the interest rate efficiently.
To find the principal amount (p) and the rate of interest (r), we know that:
- Amount after 2 years: A2 = Rs. 5100.5
- Amount after 4 years: A4 = Rs. 5203
Using the formula for compound interest, we can express the amounts as follows:
Amount Formulas
- A2 = p(1 + r/100)²
- A4 = p(1 + r/100)⁴
Setting Up the Equations
From the above formulas, we can create two equations:
- Equation 1: p(1 + r/100)² = 5100.5
- Equation 2: p(1 + r/100)⁴ = 5203
Dividing the Equations
To eliminate p, we divide Equation 2 by Equation 1:
- (p(1 + r/100)⁴) / (p(1 + r/100)²) = 5203 / 5100.5
This simplifies to:
- (1 + r/100)² = 5203 / 5100.5
Calculating the Rate
Calculate the right-hand side:
- (1 + r/100)² = 1.01996 (approximately)
Taking the square root gives:
- 1 + r/100 = 1.00995
Thus, r = (1.00995 - 1) * 100 ≈ 0.995%
Finding the Principal
Substituting r back into Equation 1:
- p(1 + 0.00995)² = 5100.5
- p * 1.0199 = 5100.5
Solving for p gives:
- p ≈ 5000
Final Values
- Principal amount, p = Rs. 5000
- Rate of interest, r ≈ 0.995% per annum
This calculation provides both the principal and the interest rate efficiently.
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An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are?
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An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are?.
An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An amount p becomes rs. 5100.5 and rs. 5203 after second and fourth years respectively, at r% of interest per annum compounded annually. thus value of p and r are?.
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