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in Compound Interest by (49.2k points)
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A money lender borrows money at 4% p.a. simple interest and pays interest at the end of the year. He lends it at 6% p.a. compound interest compounded half-yearly and receives the interest at the end of the year. Thus he gains Rs 104.50 a year. The amount of money he borrows is 

(a) Rs 4500 

(b) Rs 5000

(c) Rs 5500

(d) Rs 6000

1 Answer

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Best answer

(b) Rs 5000

Let the amount of money he borrows be Rs x. Then, 

Interest paid by the money lender= \(\frac{X\times4\times1}{100}\)

= Rs \(\frac{4X}{100}\)

Interest received by the money lender

= x\(\Big[\big(1+\frac{3}{100}\big)^2-1\Big]\)

= x\(\Big[\frac{(103)^2}{(100)^2}-1\Big]\)

= x\(\Big[\frac{103^2-100^2}{10000}\Big]\)

= x\(\Big[\frac{103+100)(103-100)}{10000}\Big]\) = \(\frac{609X}{10000}\)

Given, \(\frac{609X}{10000}\)-\(\frac{4X}{100}\) = 104.50

\(\Rightarrow\) \(\frac{209X}{10000}\) = 104.50

\(\Rightarrow\) 209x = 1045000

\(\Rightarrow\) x = \(\frac{1045000}{209}\) = Rs 5000.

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