₹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?
Answer & explanation
Correct answer: option 3
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