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The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?
- a)200/7
- b)100/7
- c)300/7
- d)400/7
Correct answer is option 'A'. Can you explain this answer?
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The difference of compound interest and simple interest for 3 years an...
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The difference of compound interest and simple interest for 3 years an...
Given,
Ratio of difference of compound interest and simple interest for 3 years and 2 years = 23:7
Let P be the principal amount, r% be the rate of interest per annum and n be the number of years.
The formula for simple interest is given by:
Simple Interest = (P * r * n) / 100
The formula for compound interest is given by:
Compound Interest = P * (1 + r/100)^n - P
Let the difference between compound interest and simple interest for 3 years and 2 years be D1 and D2 respectively.
D1 = P * [(1 + r/100)^3 - 1 - (3r/100)]
D2 = P * [(1 + r/100)^2 - 1 - (2r/100)]
Dividing D1 by D2, we get:
D1/D2 = [(1 + r/100)^3 - 1 - (3r/100)] / [(1 + r/100)^2 - 1 - (2r/100)]
Simplifying the above equation, we get:
D1/D2 = (1 + r/100) - (1/[(1 + r/100)^2 - 1 - (2r/100)])
Let (1 + r/100) = x. Substituting this in the above equation, we get:
D1/D2 = x - (1/(x^2 - 1 - (2x - 2)))
D1/D2 = x - (1/[(x-1)^2 - 2])
Let (D1/D2) = 23/7. Substituting this in the above equation, we get:
23/7 = x - (1/[(x-1)^2 - 2])
Solving the above equation, we get:
x = 2
Therefore, (1 + r/100) = 2
r/100 = 1
r = 100/7 %
Hence, the rate of interest per annum is 100/7 %.
Ratio of difference of compound interest and simple interest for 3 years and 2 years = 23:7
Let P be the principal amount, r% be the rate of interest per annum and n be the number of years.
The formula for simple interest is given by:
Simple Interest = (P * r * n) / 100
The formula for compound interest is given by:
Compound Interest = P * (1 + r/100)^n - P
Let the difference between compound interest and simple interest for 3 years and 2 years be D1 and D2 respectively.
D1 = P * [(1 + r/100)^3 - 1 - (3r/100)]
D2 = P * [(1 + r/100)^2 - 1 - (2r/100)]
Dividing D1 by D2, we get:
D1/D2 = [(1 + r/100)^3 - 1 - (3r/100)] / [(1 + r/100)^2 - 1 - (2r/100)]
Simplifying the above equation, we get:
D1/D2 = (1 + r/100) - (1/[(1 + r/100)^2 - 1 - (2r/100)])
Let (1 + r/100) = x. Substituting this in the above equation, we get:
D1/D2 = x - (1/(x^2 - 1 - (2x - 2)))
D1/D2 = x - (1/[(x-1)^2 - 2])
Let (D1/D2) = 23/7. Substituting this in the above equation, we get:
23/7 = x - (1/[(x-1)^2 - 2])
Solving the above equation, we get:
x = 2
Therefore, (1 + r/100) = 2
r/100 = 1
r = 100/7 %
Hence, the rate of interest per annum is 100/7 %.
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The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer?
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The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer?.
The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer? for Teaching 2025 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Teaching 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The difference of compound interest and simple interest for 3 years and for 2 years are in ratio 23: 7 respectively. What is rate of interest per annum (in %)?a)200/7b)100/7c)300/7d)400/7Correct answer is option 'A'. Can you explain this answer?.
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