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Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.?
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Nihal took a loan at 5% simple interest for three years and lent it at...
Given:
- Loan taken by Nihal at 5% simple interest for three years.
- Loan lent by Nihal at 5% compound interest, compounded annually for three years.
- Profit made by Nihal is Rs.76.25.
To find:
- Principal amount.
Solution:
Step 1: Calculate the interest earned from lending the money.
- Let the principal amount be P.
- Rate of interest = 5%
- Time = 3 years
- Compound Interest formula: A = P(1 + r/n)^(nt)
- Here, A is the amount after 3 years.
- A = P(1 + 0.05/1)^(1*3)
- A = P(1.05)^3
- A = 1.157625P
- Interest earned = A - P
- Interest earned = (1.157625P - P)
- Interest earned = 0.157625P
Step 2: Calculate the interest paid on the loan.
- Rate of interest = 5%
- Time = 3 years
- Simple Interest formula: SI = (P * r * t) / 100
- SI = (P * 5 * 3) / 100
- SI = 0.15P
Step 3: Calculate the profit.
- Profit = Interest earned - Interest paid
- Rs.76.25 = 0.157625P - 0.15P
- Rs.76.25 = 0.007625P
- P = Rs.76.25 / 0.007625
- P = Rs.10,000
Answer:
- The principal amount is Rs.10,000.
- Loan taken by Nihal at 5% simple interest for three years.
- Loan lent by Nihal at 5% compound interest, compounded annually for three years.
- Profit made by Nihal is Rs.76.25.
To find:
- Principal amount.
Solution:
Step 1: Calculate the interest earned from lending the money.
- Let the principal amount be P.
- Rate of interest = 5%
- Time = 3 years
- Compound Interest formula: A = P(1 + r/n)^(nt)
- Here, A is the amount after 3 years.
- A = P(1 + 0.05/1)^(1*3)
- A = P(1.05)^3
- A = 1.157625P
- Interest earned = A - P
- Interest earned = (1.157625P - P)
- Interest earned = 0.157625P
Step 2: Calculate the interest paid on the loan.
- Rate of interest = 5%
- Time = 3 years
- Simple Interest formula: SI = (P * r * t) / 100
- SI = (P * 5 * 3) / 100
- SI = 0.15P
Step 3: Calculate the profit.
- Profit = Interest earned - Interest paid
- Rs.76.25 = 0.157625P - 0.15P
- Rs.76.25 = 0.007625P
- P = Rs.76.25 / 0.007625
- P = Rs.10,000
Answer:
- The principal amount is Rs.10,000.
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Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.?
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Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.?.
Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Nihal took a loan at 5% simple interest for three years and lent it at 5% compound interest, compounded annually, for the same period. As a result he made a profit of Rs.76.25. Find the principal.?.
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