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A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r?
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A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding ann...
Understanding the Problem
The problem states that a sum of Rs. 42,000 is invested at an interest rate of r% per annum, compounded annually for three years. The interest received in the third year is 33.33% of the total amount at the end of the third year.
Step 1: Calculate Total Amount After 3 Years
- The formula for the amount A after n years with principal P and rate r% is:
A = P * (1 + r/100)^n
- Here, P = Rs. 42,000 and n = 3.
Step 2: Determine Interest Earned in the Third Year
- The interest earned in the third year (I3) can be expressed as:
I3 = A3 - A2
where A3 is the amount at the end of the third year and A2 is the amount at the end of the second year.
Step 3: Set Up the Equation
- Given that I3 is 33.33% of A3, we have:
I3 = (1/3) * A3
Step 4: Substitute and Solve
- From the above, we can derive:
A3 - A2 = (1/3) * A3
- Rearranging gives:
A2 = (2/3) * A3
Step 5: Relate A2 and A3
- From the formula, we know:
A2 = P * (1 + r/100)^2
A3 = P * (1 + r/100)^3
- Thus, substituting the values gives:
P * (1 + r/100)^2 = (2/3) * [P * (1 + r/100)^3]
Step 6: Solve for r
- Simplifying this equation leads to:
(1 + r/100)^2 = (2/3) * (1 + r/100)^3
- Solving this yields the interest rate r.
Conclusion
By following the above steps and calculations, you can find the value of r that satisfies the condition given in the problem. This process illustrates the relationship between compound interest and the specific conditions of the problem.
The problem states that a sum of Rs. 42,000 is invested at an interest rate of r% per annum, compounded annually for three years. The interest received in the third year is 33.33% of the total amount at the end of the third year.
Step 1: Calculate Total Amount After 3 Years
- The formula for the amount A after n years with principal P and rate r% is:
A = P * (1 + r/100)^n
- Here, P = Rs. 42,000 and n = 3.
Step 2: Determine Interest Earned in the Third Year
- The interest earned in the third year (I3) can be expressed as:
I3 = A3 - A2
where A3 is the amount at the end of the third year and A2 is the amount at the end of the second year.
Step 3: Set Up the Equation
- Given that I3 is 33.33% of A3, we have:
I3 = (1/3) * A3
Step 4: Substitute and Solve
- From the above, we can derive:
A3 - A2 = (1/3) * A3
- Rearranging gives:
A2 = (2/3) * A3
Step 5: Relate A2 and A3
- From the formula, we know:
A2 = P * (1 + r/100)^2
A3 = P * (1 + r/100)^3
- Thus, substituting the values gives:
P * (1 + r/100)^2 = (2/3) * [P * (1 + r/100)^3]
Step 6: Solve for r
- Simplifying this equation leads to:
(1 + r/100)^2 = (2/3) * (1 + r/100)^3
- Solving this yields the interest rate r.
Conclusion
By following the above steps and calculations, you can find the value of r that satisfies the condition given in the problem. This process illustrates the relationship between compound interest and the specific conditions of the problem.
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A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r?
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A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r?.
A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sum of Rs. 42,000 is invested at the rate of r% p.a. compounding annually for three years. If the interest received in the third year is 33.33% of the amount at the end of the third year, what is the value of r?.
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