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 ?
Answer & explanation
Correct answer: option 4
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