What is the difference between the compound interest on ₹10,000 for $1\frac{1}{2}$ years at 4% per annum compounded yearly and half-yearly ?

₹4.08

1st case,

Interest is compounded anually ,

For 1/2nd year

rate = \(\frac{4}{2}\)% = 2%

From the formula for compound interest, we know,

C.I = P(1+$\frac{R}{100})^t$– P

= 10000 × \(\frac{104}{100}\) × \(\frac{102}{100}\) - 10000

= 10000 × \(\frac{26}{25}\) × \(\frac{51}{50}\) - 10000

= 10608 - 10000

= 608

2nd case,

Interest is compounded half yearly ,

Rate = \(\frac{4}{2}\)% = 2%

C.I = P(1+$\frac{R}{100})^t$– P

= 10000 [  1 + \(\frac{2}{100}\) ]³ - 10000

= 10000 × \(\frac{51}{50}\) × \(\frac{51}{50}\) × \(\frac{51}{50}\) - 10000

= 10612.08 - 10000

= 612.08

Required difference = 612.08 - 608

= Rs. 4.08