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 half yearly and receives the interest at the end of the year. In this way, he gains ₹ 104.50 a year. The amount of money he borrows, is

Let the borrowed amount be y
According to the question,

1 +

− 1

−

y × 4 × 1

= 104.50

100

[∵ Interest is compounded half yearly]
⇒ y [(1.03)² – 1] – 0.04y = 104.50
⇒ 0.0609y – 0.04y = 104.50
⇒ 0.0209y = 104.5

⇒ y =	104.5	= ₹ 5000
	0.0209