What is the difference between the compound interest (in ₹) compounded yearly and compounded half yearly for 18 months at 20% per annum on a sum of ₹12,000?
Answer & explanation
Correct answer: option 2
We know ,
Compound interest = Principal × ( 1 + \(\frac{rate }{100}\) )t - Principal
Required difference b/w compound interest compounded half yearly and compound interest yearly.
CI ( half yearly ) - CI ( yearly ) = Principal × ( 1 + \(\frac{rate }{2 ×100}\) )2t - Principal × ( 1 + \(\frac{rate }{100}\) )t
= 12000× ( 1 + \(\frac{20 }{200}\) )3 - 12000 × ( 1 + \(\frac{20 }{100}\) )1.5
= 12000 × [ ( 1 + \(\frac{20 }{200}\) )3 - ( 1 + \(\frac{20 }{100}\) )1.5 ]
= 12000 × [ ( 1 + \(\frac{1 }{10}\) )3 - ( 1 + \(\frac{1 }{5}\) )1.5 ]
= 12000 × [ \(\frac{11 }{10}\) × \(\frac{11 }{10}\) × \(\frac{11 }{10}\) - \(\frac{6 }{5}\) × \(\frac{6 }{5}\)1.5 ]
= 132