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If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest?
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If sum of money compounded annually becomes 1140 in 2 years and 1710 i...
Solution:
Given,
Sum of money compounded annually becomes 1140 in 2 years
Sum of money compounded annually becomes 1710 in 3 years
Let the principal amount be P and the rate of interest be R.
We need to find the value of R.
Using the formula for compound interest, we know that:
Amount = P(1 + R/100)^n
where,
P = Principal amount
R = Rate of interest
n = Number of years
We can use the above formula to form two equations:
Equation 1: 1140 = P(1 + R/100)^2
Equation 2: 1710 = P(1 + R/100)^3
Solving for P in both equations:
P = 1140 / (1 + R/100)^2
P = 1710 / (1 + R/100)^3
Equating P in both equations:
1140 / (1 + R/100)^2 = 1710 / (1 + R/100)^3
Taking LCM and simplifying:
1710(1 + R/100) = 1140 * (1 + R/100)^2
Dividing both sides by 1140:
1 + R/100 = √(1710/1140)
1 + R/100 = √(3/2)
R/100 = √(3/2) – 1
R = 100(√(3/2) – 1)
R = 23.09 (approx.)
Therefore, the rate of interest is 23.09%.
Note: The above calculation can be done using logarithms or trial and error method.
Given,
Sum of money compounded annually becomes 1140 in 2 years
Sum of money compounded annually becomes 1710 in 3 years
Let the principal amount be P and the rate of interest be R.
We need to find the value of R.
Using the formula for compound interest, we know that:
Amount = P(1 + R/100)^n
where,
P = Principal amount
R = Rate of interest
n = Number of years
We can use the above formula to form two equations:
Equation 1: 1140 = P(1 + R/100)^2
Equation 2: 1710 = P(1 + R/100)^3
Solving for P in both equations:
P = 1140 / (1 + R/100)^2
P = 1710 / (1 + R/100)^3
Equating P in both equations:
1140 / (1 + R/100)^2 = 1710 / (1 + R/100)^3
Taking LCM and simplifying:
1710(1 + R/100) = 1140 * (1 + R/100)^2
Dividing both sides by 1140:
1 + R/100 = √(1710/1140)
1 + R/100 = √(3/2)
R/100 = √(3/2) – 1
R = 100(√(3/2) – 1)
R = 23.09 (approx.)
Therefore, the rate of interest is 23.09%.
Note: The above calculation can be done using logarithms or trial and error method.
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If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest?.
If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If sum of money compounded annually becomes 1140 in 2 years and 1710 in 3 years then what is the rate of interest?.
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