A money - lender borrows money at 4% per annum and pays the
A money - lender borrows money at 4% per annum and pays the interest at the end of the year. He lends it at 6% per annum compound interest compounded halfy early and receives the interest at the end of the year. In this way, he gains Rs.104.50 a year. The amount of money he borrows, is
ARs.6,000
BRs.5,500
CRs.5,000
DRs.4,500
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Answer is : Rs.5,000
Let he borrowed Rs x
borrows money at 4% per annum and pays the interest at the end of the year
Amount he has to return = \(\frac{104x}{100}\)
Amount he will get = \(\big(1+\frac{3}{100}\big)^2 = \frac{10609}{10000}x\)
His gain = \(\frac{10609}{10000}x = \frac{104}{100}x = 104.50\)
\(x\big(\frac{10609}{10000}-\frac{104}{100}\big)=104.50\)
\(x\big(\frac{10609}{10000}-\frac{10400}{10000}\big) = 104.50\)
\(x\big(\frac{10609-10400}{10000}\big)=104.50\)
\(x\big(\frac{209}{10000}\big)=104.50\)
\(x=\frac{104.50 * 10000}{209}\)
\(x = \text{Rs }5000\)
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