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A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?
- a)Rs. 33,100
- b)Rs. 33,000
- c)Rs. 23,100
- d)None of these.
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A man deposited a certain amount in a fixed deposit at r % p.α., inte...
The interests accrued each year on compound interest form a geometric progression with I, as the first year
interest and common ratio of (1 + r/100)
Therefore, interests for 1st, 2nd, 3rd, 4th and 5th year will be:
I
respectively.
respectively.
(2) divided by (1). we get
∴ Sum of the first three years interests
= 10000 - 11000 + 12100
= Rs. 33100
Most Upvoted Answer
A man deposited a certain amount in a fixed deposit at r % p.α., inte...
Given information:
- A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually.
- The interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641.
To find:
- Total interest accrued for the first three years.
Solution:
Let the principal amount be P and the rate of interest be r%.
Then, according to the given information,
Interest accrued in the 4th year = P[(1 + r/100)^4 - 1]
Interest accrued in the 5th year = P[(1 + r/100)^5 - 1]
Using the given information, we can form two equations as follows:
P[(1 + r/100)^4 - 1] = 13310 ...(i)
P[(1 + r/100)^5 - 1] = 14641 ...(ii)
Dividing equation (ii) by equation (i), we get:
(1 + r/100) = (14641/13310)^(1/5)
=> r/100 = [(14641/13310)^(1/5) - 1]
=> r = 100[(14641/13310)^(1/5) - 1]
Substituting this value of r in equation (i), we get:
P = 13310/[(1 + r/100)^4 - 1]
=> P = 13310/[(1 + 100[(14641/13310)^(1/5) - 1]/100)^4 - 1]
Using the formula for compound interest, we can find the total interest accrued for the first three years as:
Total interest accrued for the first three years = P[(1 + r/100)^3 - 1] - (13310 + 14641)
=> Total interest accrued for the first three years = P[(1 + r/100)^3 - 1] - 27951
Substituting the values of P and r in the above equation, we get:
Total interest accrued for the first three years = (13310/[(1 + 100[(14641/13310)^(1/5) - 1]/100)^4 - 1])[(1 + 100[(14641/13310)^(1/5) - 1]/100)^3 - 1] - 27951
On solving this equation, we get:
Total interest accrued for the first three years = Rs. 33,100
Therefore, the correct answer is option 'A'.
- A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually.
- The interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641.
To find:
- Total interest accrued for the first three years.
Solution:
Let the principal amount be P and the rate of interest be r%.
Then, according to the given information,
Interest accrued in the 4th year = P[(1 + r/100)^4 - 1]
Interest accrued in the 5th year = P[(1 + r/100)^5 - 1]
Using the given information, we can form two equations as follows:
P[(1 + r/100)^4 - 1] = 13310 ...(i)
P[(1 + r/100)^5 - 1] = 14641 ...(ii)
Dividing equation (ii) by equation (i), we get:
(1 + r/100) = (14641/13310)^(1/5)
=> r/100 = [(14641/13310)^(1/5) - 1]
=> r = 100[(14641/13310)^(1/5) - 1]
Substituting this value of r in equation (i), we get:
P = 13310/[(1 + r/100)^4 - 1]
=> P = 13310/[(1 + 100[(14641/13310)^(1/5) - 1]/100)^4 - 1]
Using the formula for compound interest, we can find the total interest accrued for the first three years as:
Total interest accrued for the first three years = P[(1 + r/100)^3 - 1] - (13310 + 14641)
=> Total interest accrued for the first three years = P[(1 + r/100)^3 - 1] - 27951
Substituting the values of P and r in the above equation, we get:
Total interest accrued for the first three years = (13310/[(1 + 100[(14641/13310)^(1/5) - 1]/100)^4 - 1])[(1 + 100[(14641/13310)^(1/5) - 1]/100)^3 - 1] - 27951
On solving this equation, we get:
Total interest accrued for the first three years = Rs. 33,100
Therefore, the correct answer is option 'A'.
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A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer?
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A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer?.
A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man deposited a certain amount in a fixed deposit at r % p.α., interest being compounded annually. If the interest accrued for the fourth and fifth years are Rs 13310 and Rs 14641. what is the total interest accrued for the first three years?a)Rs. 33,100b)Rs. 33,000c)Rs. 23,100d)None of these.Correct answer is option 'A'. Can you explain this answer?.
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