₹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 ?

₹67.5

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