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A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?
Correct answer is '40750'. Can you explain this answer?
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A man invested Rs. 80000 in a bond which gives 10% p.a interest compou...
As the rate of interest is increasing by 20% annually, the rate of interest per half year increased by 10% over previous year.
The required interest that has been accrued is 40,750.
The required interest that has been accrued is 40,750.
Most Upvoted Answer
A man invested Rs. 80000 in a bond which gives 10% p.a interest compou...
**Given information:**
- Principal amount (P) = Rs. 80000
- Annual interest rate = 10%
- Interest is compounded half-yearly
- Annual interest rate is increased by 20% at the end of every half-year
**Solution:**
To calculate the interest earned for one and a half years, we need to break it down into two parts:
1. Interest earned for the first year (two half-year periods)
2. Interest earned for the second half-year period
**1. Interest earned for the first year:**
Since the interest is compounded half-yearly, the annual interest rate needs to be divided by 2 to get the half-yearly interest rate.
Half-yearly interest rate = (10% / 2) = 5%
For the first half-year period:
Principal amount (P1) = Rs. 80000
Half-yearly interest rate (r1) = 5%
Number of half-year periods (n1) = 2
Using the formula for compound interest:
A1 = P1 * (1 + r1/100)^n1
A1 = 80000 * (1 + 5/100)^2
A1 = 80000 * (1.05)^2
A1 = 80000 * 1.1025
A1 = Rs. 88200
The interest earned for the first half-year period = A1 - P1
Interest1 = 88200 - 80000
Interest1 = Rs. 8200
For the second half-year period:
Principal amount (P2) = A1 (final amount of the first half-year period) = Rs. 88200
Half-yearly interest rate (r2) = (10% + 20%) / 2 = 15%
Number of half-year periods (n2) = 1
Using the same formula for compound interest:
A2 = P2 * (1 + r2/100)^n2
A2 = 88200 * (1 + 15/100)^1
A2 = 88200 * (1.15)^1
A2 = 88200 * 1.15
A2 = Rs. 101130
The interest earned for the second half-year period = A2 - P2
Interest2 = 101130 - 88200
Interest2 = Rs. 12930
**2. Interest earned for the second half-year period:**
Principal amount (P3) = A2 (final amount of the second half-year period) = Rs. 101130
Half-yearly interest rate (r3) = (10% + 20%) / 2 = 15%
Number of half-year periods (n3) = 1
Using the same formula for compound interest:
A3 = P3 * (1 + r3/100)^n3
A3 = 101130 * (1 + 15/100)^1
A3 = 101130 * (1.15)^1
A3 = 101130 * 1.15
A3 = Rs. 116299.50
The interest earned for the third half-year period = A3 - P3
Interest3 = 116299.50 - 101130
Interest3 = Rs. 15169.50
**Total interest
- Principal amount (P) = Rs. 80000
- Annual interest rate = 10%
- Interest is compounded half-yearly
- Annual interest rate is increased by 20% at the end of every half-year
**Solution:**
To calculate the interest earned for one and a half years, we need to break it down into two parts:
1. Interest earned for the first year (two half-year periods)
2. Interest earned for the second half-year period
**1. Interest earned for the first year:**
Since the interest is compounded half-yearly, the annual interest rate needs to be divided by 2 to get the half-yearly interest rate.
Half-yearly interest rate = (10% / 2) = 5%
For the first half-year period:
Principal amount (P1) = Rs. 80000
Half-yearly interest rate (r1) = 5%
Number of half-year periods (n1) = 2
Using the formula for compound interest:
A1 = P1 * (1 + r1/100)^n1
A1 = 80000 * (1 + 5/100)^2
A1 = 80000 * (1.05)^2
A1 = 80000 * 1.1025
A1 = Rs. 88200
The interest earned for the first half-year period = A1 - P1
Interest1 = 88200 - 80000
Interest1 = Rs. 8200
For the second half-year period:
Principal amount (P2) = A1 (final amount of the first half-year period) = Rs. 88200
Half-yearly interest rate (r2) = (10% + 20%) / 2 = 15%
Number of half-year periods (n2) = 1
Using the same formula for compound interest:
A2 = P2 * (1 + r2/100)^n2
A2 = 88200 * (1 + 15/100)^1
A2 = 88200 * (1.15)^1
A2 = 88200 * 1.15
A2 = Rs. 101130
The interest earned for the second half-year period = A2 - P2
Interest2 = 101130 - 88200
Interest2 = Rs. 12930
**2. Interest earned for the second half-year period:**
Principal amount (P3) = A2 (final amount of the second half-year period) = Rs. 101130
Half-yearly interest rate (r3) = (10% + 20%) / 2 = 15%
Number of half-year periods (n3) = 1
Using the same formula for compound interest:
A3 = P3 * (1 + r3/100)^n3
A3 = 101130 * (1 + 15/100)^1
A3 = 101130 * (1.15)^1
A3 = 101130 * 1.15
A3 = Rs. 116299.50
The interest earned for the third half-year period = A3 - P3
Interest3 = 116299.50 - 101130
Interest3 = Rs. 15169.50
**Total interest
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A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer?
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A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer?.
A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer?.
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A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer?, a detailed solution for A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer? has been provided alongside types of A man invested Rs. 80000 in a bond which gives 10% p.a interest compounded half yearly. If the annual rate of interest is increased by 20% at the end of every half year. What will be the interest earned (in Rs.) for one and a half years?Correct answer is '40750'. Can you explain this answer? theory, EduRev gives you an
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