The difference between the compound interest (compounding half yearly) for 1 year and the simple interest for 1 year on a certain sum lent out at the annual rate of 10 percent is Rs.25. What is the sum?

Rs. 10000

We know,

Simple interest = \(\frac{Principal × Rate ×Time  }{100}\) 

= \(\frac{Principal × 10 ×1  }{100}\)

= 0.1 × Principal

Compound interest = Principal × ( 1 + \(\frac{rate }{100}\) )^t - Principal

= Principal × ( 1 + \(\frac{5 }{100}\) )² - Principal

= 0.1025 × Principal

ATQ,

( 0,1025 × Principal - 0.1 × Principal ) = 25

0.0025 × Principal = 25

Principal = Rs.10000