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A sum of money is borrowed and paid back in two annual instalments of Rs. 882 each allowing 5% compound interest. The sum borrowed was
- a)Rs. 1620
- b)Rs. 1640
- c)Rs. 1680
- d)Rs. 1700
Correct answer is option 'B'. Can you explain this answer?
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A sum of money is borrowed and paid back in two annual instalments of ...
Solution:
Let's assume the sum borrowed is 'P' rupees.
Given that the sum is paid back in two annual instalments of Rs. 882 each.
Using compound interest formula, we can calculate the amount after one year:
Amount after 1st year = P(1 + 5/100) = P(21/20)
Now, the remaining amount after the 1st installment is deducted:
Remaining amount = P(21/20) - 882
Amount after 2nd year = Remaining amount(1 + 5/100) = (P(21/20) - 882)(21/20)
According to the given conditions, the remaining amount after the 2nd installment should be zero.
So, we can write the equation as:
(P(21/20) - 882)(21/20) = 0
Simplifying the equation:
(P(21/20) - 882)(21/20) = 0
(P(21/20) - 882) = 0
P(21/20) = 882
P = 882 * (20/21)
P = 840
Therefore, the sum borrowed is Rs. 840.
But none of the given options matches with this answer.
Hence, the given information is not sufficient to find the exact sum borrowed.
Therefore, the correct answer is 'None of the above'.
Let's assume the sum borrowed is 'P' rupees.
Given that the sum is paid back in two annual instalments of Rs. 882 each.
Using compound interest formula, we can calculate the amount after one year:
Amount after 1st year = P(1 + 5/100) = P(21/20)
Now, the remaining amount after the 1st installment is deducted:
Remaining amount = P(21/20) - 882
Amount after 2nd year = Remaining amount(1 + 5/100) = (P(21/20) - 882)(21/20)
According to the given conditions, the remaining amount after the 2nd installment should be zero.
So, we can write the equation as:
(P(21/20) - 882)(21/20) = 0
Simplifying the equation:
(P(21/20) - 882)(21/20) = 0
(P(21/20) - 882) = 0
P(21/20) = 882
P = 882 * (20/21)
P = 840
Therefore, the sum borrowed is Rs. 840.
But none of the given options matches with this answer.
Hence, the given information is not sufficient to find the exact sum borrowed.
Therefore, the correct answer is 'None of the above'.
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A sum of money is borrowed and paid back in two annual instalments of Rs. 882 each allowing 5% compound interest. The sum borrowed wasa)Rs. 1620 b)Rs. 1640c)Rs. 1680 d)Rs. 1700Correct answer is option 'B'. Can you explain this answer?
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