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 half yearly and receives the interest at the end of they year. In this way, he gains Rs. 104.50 a year. The amount of money he borrows, is:
Rs. 6000
Rs. 5,500
Rs. 3,000
Rs. 4, 500
Rs. 5,000
Solution
Let the borrowed amount be $x$
According to the question,
$x\left[\left(1+\dfrac{3}{100}\right)^2-1\right]-\dfrac{x\times 4\times 1}{100} = 104.50$
[$\because$ Interest is compounded half yearly]
$\Rightarrow x[(1.03)^2-1]-0.04x = 104.50$
$\Rightarrow 0.0609x - 0.04x = 104.50$
$\Rightarrow 0.0209x = 104.5$
$\Rightarrow x = \dfrac{104.5}{0.0209}=$ Rs.5000