A bank offers 20% compound interest calculated on half year basis. A customer deposits Rs 9200 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is

Principal = Rs. 9,200 and Rate = 20%

Amount on half yearly basis= $$P (1 + \frac{R}{2 \times100})^{2 \times T}$$

= $$[9200 (1 + \frac{20}{2 \times 100})^{2 \times 1}] + [9200 (1 + \frac{20}{2 \times 100})^{2 \times \frac{1}{2}}]$$

= $$[9200 \times (\frac{11}{10})^2] + [9200 \times \frac{11}{10}]$$

= $$[92 \times 121] + [920 \times 11]$$

= $$(92 \times 11) \times (11 + 10)$$

= $$92 \times 11 \times 21 = Rs. 21,252$$

$$\therefore$$ Compound Interest = Rs.(21,252 - 18,400) = Rs. 2,852