₹15,000 is lent for one year at the rate of 20% per annum, the interest being compounded annually. If the compounding of the interest is done half - yearly, then how much more interest will be obtained at the end of the one-year period on the same initial sum?

₹150

First case ,

Interest is compounded annually ,

Compound interest of 1 year = 15000 × \(\frac{20}{100}\) = 3000

2nd case,

Interest is compounded half-yearly,

New rate = \(\frac{20}{2}\) % = 10%

Compound interest = P(1+$\frac{R}{100})^t$– P

= 15000 × [ 1 + \(\frac{10}{100}\) ]² - 15000

= 15000 × [  \(\frac{11}{10}\) × \(\frac{11}{10}\) - 1 ]

= 15000 × [  \(\frac{21}{100}\) ]

= 3150

So, Required difference = 3150 - 3000

= Rs. 150