A money lender borrows money at 4% p.a. simple interest and pays inter

1.	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
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.

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

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.