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Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.?
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Motilal deposites rupees 16000 in a bank which pays interest at the ra...
Understanding the Problem
Motilal deposits a sum of rupees 16,000 in a bank that offers a compound interest rate of 20% per annum, compounded quarterly. We need to calculate the interest he will receive after one year.
Key Information
- Principal Amount (P): 16,000 rupees
- Annual Interest Rate (r): 20%
- Compounding Frequency (n): Quarterly (4 times a year)
- Time Period (t): 1 year
Calculating the Compound Interest
To find the compound interest, we first need to calculate the total amount (A) using the formula:
A = P * (1 + r/n)^(nt)
Where:
- A = Total amount after time period t
- P = Principal amount
- r = Annual interest rate (in decimal)
- n = Number of times interest is compounded per year
- t = Time in years
Step-by-Step Calculation
1. Convert the interest rate from percentage to decimal:
r = 20% = 0.20
2. Substitute the values into the formula:
A = 16000 * (1 + 0.20/4)^(4*1)
A = 16000 * (1 + 0.05)^(4)
A = 16000 * (1.05)^4
3. Calculate (1.05)^4:
(1.05)^4 = 1.21550625
4. Now calculate A:
A = 16000 * 1.21550625
A ≈ 19448.10 rupees
Calculating the Interest Received
To find the interest earned (I), subtract the principal from the total amount:
I = A - P
I = 19448.10 - 16000
I ≈ 3448.10 rupees
Conclusion
Motilal will receive approximately 3,448.10 rupees as interest after one year.
Motilal deposits a sum of rupees 16,000 in a bank that offers a compound interest rate of 20% per annum, compounded quarterly. We need to calculate the interest he will receive after one year.
Key Information
- Principal Amount (P): 16,000 rupees
- Annual Interest Rate (r): 20%
- Compounding Frequency (n): Quarterly (4 times a year)
- Time Period (t): 1 year
Calculating the Compound Interest
To find the compound interest, we first need to calculate the total amount (A) using the formula:
A = P * (1 + r/n)^(nt)
Where:
- A = Total amount after time period t
- P = Principal amount
- r = Annual interest rate (in decimal)
- n = Number of times interest is compounded per year
- t = Time in years
Step-by-Step Calculation
1. Convert the interest rate from percentage to decimal:
r = 20% = 0.20
2. Substitute the values into the formula:
A = 16000 * (1 + 0.20/4)^(4*1)
A = 16000 * (1 + 0.05)^(4)
A = 16000 * (1.05)^4
3. Calculate (1.05)^4:
(1.05)^4 = 1.21550625
4. Now calculate A:
A = 16000 * 1.21550625
A ≈ 19448.10 rupees
Calculating the Interest Received
To find the interest earned (I), subtract the principal from the total amount:
I = A - P
I = 19448.10 - 16000
I ≈ 3448.10 rupees
Conclusion
Motilal will receive approximately 3,448.10 rupees as interest after one year.
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Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.?
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Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.? 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 Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.?.
Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.? 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 Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Motilal deposites rupees 16000 in a bank which pays interest at the rate of 20% per annum compounded quarterly. Find the interest received by Motilal after 1 year.?.
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