Question

A money lender borrows money at $14\%$ 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 1

The correct option is B Rs. $5000$

Let the amount of money he borrows be Rs. $x$

Then Interest paid by the money lender $=\frac{x\times 4\times 1}{100}=$ Rs. $\frac{4x}{100}$
Interest received by the money lender $=x[{(1+\frac{3}{100})}^2-1]$
$=x[\frac{(103{)}^2}{(100{)}^2}-1]=x\left[\frac{{103}^2-{100}^2}{10000}\right]$
$=x\left[\frac{(103+100)(103-100)}{10000}\right]=\frac{609x}{10000}$

Given, $\frac{609x}{1000}-\frac{4x}{100}=104.50$
$\Rightarrow \frac{209x}{10000}=104.50$

$\Rightarrow 209x=1045000$

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