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?

132

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