₹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?

₹12,000 is lent for one year at the rate of 15% per annum, the interest being compounded annually.

compound interest for one year = 12000 of 15%

= $$12000\times\frac{15}{100}$$

= ₹1800

If the compounding of the interest is done half yearly.

compound interest for one year = 12000 of (100+7.5)% of (100+7.5)% - 12000

= 12000 of 107.5% of 107.5% - 12000

= $$12000\left[\frac{107.5}{100}\times\frac{107.5}{100}-1\right]$$

= $$12000\left[\frac{11556.25}{10000}-1\right]$$

= $$12000\left[1.155625-1\right]$$

= ₹1867.5

Increase in the interest at the end of the one-year period on the same initial sum when interest is calculated on half yearly = ₹1867.5-₹1800

= ₹67.5