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Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly?
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Indu lent out rupees 18000 for 2 years at 20% per annum compounded ann...
Introduction
Indu's investment of rupees 18000 for 2 years at a 20% per annum interest rate can yield different returns depending on the compounding frequency. We will calculate the total amount earned with both annual and half-yearly compounding.
1. Interest Compounded Annually
- Principal Amount (P): 18000
- Rate of Interest (r): 20% per annum
- Time (t): 2 years
The formula for compound interest is:
Amount = P(1 + r/n)^(nt)
Where n is the number of times interest is compounded per year. For annual compounding, n = 1.
- Calculation:
- Amount = 18000(1 + 0.20/1)^(1*2)
- Amount = 18000(1 + 0.20)^2
- Amount = 18000 * (1.20)^2
- Amount = 18000 * 1.44
- Total Amount = 25920
- Interest Earned: Total Amount - Principal = 25920 - 18000 = 7920
2. Interest Compounded Half-Yearly
- Principal Amount (P): 18000
- Rate of Interest (r): 20% per annum = 10% per half-year
- Time (t): 2 years = 4 half-year periods (n = 2)
- Calculation:
- Amount = 18000(1 + 0.10/1)^(2*2)
- Amount = 18000(1 + 0.10)^4
- Amount = 18000 * (1.10)^4
- Amount = 18000 * 1.4641
- Total Amount = 26353.80
- Interest Earned: Total Amount - Principal = 26353.80 - 18000 = 8353.80
3. Difference in Earnings
- Difference: 8353.80 - 7920 = 433.80
Conclusion
Indu could earn rupees 433.80 more if the interest were compounded half-yearly instead of annually. This illustrates the significant impact of compounding frequency on investment returns.
Indu's investment of rupees 18000 for 2 years at a 20% per annum interest rate can yield different returns depending on the compounding frequency. We will calculate the total amount earned with both annual and half-yearly compounding.
1. Interest Compounded Annually
- Principal Amount (P): 18000
- Rate of Interest (r): 20% per annum
- Time (t): 2 years
The formula for compound interest is:
Amount = P(1 + r/n)^(nt)
Where n is the number of times interest is compounded per year. For annual compounding, n = 1.
- Calculation:
- Amount = 18000(1 + 0.20/1)^(1*2)
- Amount = 18000(1 + 0.20)^2
- Amount = 18000 * (1.20)^2
- Amount = 18000 * 1.44
- Total Amount = 25920
- Interest Earned: Total Amount - Principal = 25920 - 18000 = 7920
2. Interest Compounded Half-Yearly
- Principal Amount (P): 18000
- Rate of Interest (r): 20% per annum = 10% per half-year
- Time (t): 2 years = 4 half-year periods (n = 2)
- Calculation:
- Amount = 18000(1 + 0.10/1)^(2*2)
- Amount = 18000(1 + 0.10)^4
- Amount = 18000 * (1.10)^4
- Amount = 18000 * 1.4641
- Total Amount = 26353.80
- Interest Earned: Total Amount - Principal = 26353.80 - 18000 = 8353.80
3. Difference in Earnings
- Difference: 8353.80 - 7920 = 433.80
Conclusion
Indu could earn rupees 433.80 more if the interest were compounded half-yearly instead of annually. This illustrates the significant impact of compounding frequency on investment returns.
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Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly?
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Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly? 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 Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly?.
Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly? 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 Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Indu lent out rupees 18000 for 2 years at 20% per annum compounded annually. How much more could she earn, if the interest were compounded half yearly?.
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