What is the difference between the compound interests on ₹10000 for two years at 20% per annum when the interests are compounded half-yearly and yearly respectively?

₹241

Interest is compounded half yearly

So, Actual rate of interest = \(\frac{20}{2}\)% = 10%

From the formula for compound interest, we know,

C.I = P(1+$\frac{R}{100})^t$– P

= 10000[ \(\frac{11}{10}\) × \(\frac{11}{10}\)× \(\frac{11}{10}\)× \(\frac{11}{10}\) - 1 ]

= 10000[ \(\frac{14641}{10000}\)  - 1 ] 

= 10000[ \(\frac{4641}{10000}\)  ]

= Rs. 4641

From the formula for compound interest, we know,

C.I = P(1+$\frac{R}{100})^t$– P

= 10000 [ 1 + \(\frac{20}{100}\) ]²- 10000

= 10000[ \(\frac{36}{25}\)  - 1 ] 

= 10000[ \(\frac{11}{25}\)  ]

= Rs. 4400

Required difference = 4641 - 4400 = Rs. 241