A bank offers 10% compound interest per half year. A customer deposits Rs. 2000 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. 2000 and Rate = 10 %

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

= $$[2000 (1 + \frac{10}{2 \times 100})^{2 \times 1}] + [2000 (1 + \frac{10}{2 \times 100})^{2 \times \frac{1}{2}}]$$

= $$[2000 \times (\frac{21}{20})^2] + [2000 \times \frac{21}{20}]$$

= $$[5 \times 441] + [100 \times 21]$$

= $$2205 + 2100 = Rs. 4,305$$

$$\therefore$$ Compound Interest = Rs.(4305 - 4000) = Rs. 305