₹12,000 is lent for one year at the rate of 15% per annum, the interest being compounded annually. If the compounding of the interest is done half- yearly, then how much more interest will be obtained at the end of the one-year period on the same initial sum ?
Answer & explanation
Correct answer: option 4
1st case,
Interest is compounded yearly ,
CI = 12000 × \(\frac{15}{100}\)
= 12000 × \(\frac{3}{20}\)
= Rs. 1800
2nd case,
Interest is compounded half yearly,
Rate of interest = \(\frac{15}{2}\)%
From the formula for compound interest, we know,
C.I = P(1+$\frac{R}{100})^t$– P
= 12000 [ 1 + \(\frac{15}{200}\) ]² - 12000
= 12000 [ \(\frac{43}{40}\) × \(\frac{43}{40}\) - 1 ]
= 12000 [ \(\frac{1849}{1600}\) - 1 ]
= 12000 [ \(\frac{249}{1600}\) ]
= Rs. 1867.5
Required difference = 1867.5 - 1800
= Rs. 67.5