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?
Answer & explanation
Correct answer: option 4
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