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Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?
- a)Rs. 500
- b)Rs. 525
- c)Rs. 550
- d)Rs. 575
- e)Rs. 60
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Jack invests Rs. 1,00,000 in a bank at some rate of interest compounde...
Let the annual interest be r%.
Interest for the first year compounded half yearly
As per the given condition, lOOOr + 2.5r2 - lOOOr = 250
r = 10Interest on Rs. 1,00,000 for two years compounded annually (r = 10% p. a. and n = 2)
= 100000 x l . l 2 - 100000 = 21,000
Interest on Rs. 1,00,000 for two years compounded half yearly (r = 5% p. a. and n = 4)
= 100000 x 1.054 - 100000 = 21,550.625
Extra interest he would get = Rs.(21,550.625 - 21,000) = Rs. 550.625 Hence, option 3.
Most Upvoted Answer
Jack invests Rs. 1,00,000 in a bank at some rate of interest compounde...
Understanding the Problem
Jack invests Rs. 1,00,000 at a certain rate, and the interest is compounded annually. When compounded half-yearly, he earns Rs. 250 more in the first year. We need to determine how much extra interest he would earn by investing half-yearly instead of annually over 2 years.
Interest Calculation for 1 Year
1. Let the rate of interest be 'r%'.
2. Interest when compounded annually:
- Amount after 1 year = 100000 * (1 + r/100)
- Interest = Amount - Principal = 100000 * (1 + r/100) - 100000 = 100000 * (r/100)
3. Interest when compounded half-yearly:
- Amount after 1 year = 100000 * (1 + r/200)² (since it compounds twice a year)
- Interest = Amount - Principal = 100000 * (1 + r/200)² - 100000
Setting the difference in interest earned in the first year to Rs. 250 gives us:
100000 * (1 + r/200)² - 100000 * (1 + r/100) = 250
Finding Extra Interest Over 2 Years
1. Interest for 2 Years (Annually):
- Amount = 100000 * (1 + r/100)²
- Interest = Amount - Principal = 100000 * (1 + r/100)² - 100000
2. Interest for 2 Years (Half-Yearly):
- Amount = 100000 * (1 + r/200)⁴
- Interest = Amount - Principal = 100000 * (1 + r/200)⁴ - 100000
The extra interest earned by compounding half-yearly for 2 years compared to annually can be calculated by finding the difference between the two interest amounts calculated above.
Conclusion
After performing the calculations, it is established that the extra interest earned in 2 years by compounding half-yearly instead of annually is approximately Rs. 550. Thus, the correct answer is option 'C'.
Jack invests Rs. 1,00,000 at a certain rate, and the interest is compounded annually. When compounded half-yearly, he earns Rs. 250 more in the first year. We need to determine how much extra interest he would earn by investing half-yearly instead of annually over 2 years.
Interest Calculation for 1 Year
1. Let the rate of interest be 'r%'.
2. Interest when compounded annually:
- Amount after 1 year = 100000 * (1 + r/100)
- Interest = Amount - Principal = 100000 * (1 + r/100) - 100000 = 100000 * (r/100)
3. Interest when compounded half-yearly:
- Amount after 1 year = 100000 * (1 + r/200)² (since it compounds twice a year)
- Interest = Amount - Principal = 100000 * (1 + r/200)² - 100000
Setting the difference in interest earned in the first year to Rs. 250 gives us:
100000 * (1 + r/200)² - 100000 * (1 + r/100) = 250
Finding Extra Interest Over 2 Years
1. Interest for 2 Years (Annually):
- Amount = 100000 * (1 + r/100)²
- Interest = Amount - Principal = 100000 * (1 + r/100)² - 100000
2. Interest for 2 Years (Half-Yearly):
- Amount = 100000 * (1 + r/200)⁴
- Interest = Amount - Principal = 100000 * (1 + r/200)⁴ - 100000
The extra interest earned by compounding half-yearly for 2 years compared to annually can be calculated by finding the difference between the two interest amounts calculated above.
Conclusion
After performing the calculations, it is established that the extra interest earned in 2 years by compounding half-yearly instead of annually is approximately Rs. 550. Thus, the correct answer is option 'C'.
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Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. Can you explain this answer?
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Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. 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 Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. Can you explain this answer?.
Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. 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 Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Jack invests Rs. 1,00,000 in a bank at some rate of interest compounded annually. If he would have invested the same amount at the same rate of interest compounded half yearly, he would have earned Rs. 250 more as an interest at the end of the first year. Approximately, how much extra interest would he earn by investing the amount compounded half yearly instead of compounded annually at the same rate of interest for 2 years?a)Rs. 500b)Rs. 525c)Rs. 550d)Rs. 575e)Rs. 60Correct answer is option 'C'. Can you explain this answer?.
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