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?
Answer & explanation
Correct answer: option 2
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