A bank offers 15% compound interest per annum compounded half-yearly. A customer deposits Rs 2400 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. 2400 and Rate = 15%

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

= $$[2400 (1 + \frac{15}{2 \times 100})^{2 \times 1}] + [2400 (1 + \frac{15}{2 \times 100})^{2 \times \frac{1}{2}}]$$

= $$[2400 \times (\frac{43}{40})^2] + [2400 \times \frac{43}{40}]$$

= $$[2400 \times \frac{43}{40}] \times [\frac{43}{40} + 1]$$

= $$(60 \times 43) \times (\frac{83}{40})$$

= $$\frac{3}{2} \times 3569 = $$Rs.$$ 5353.5$$

$$\therefore$$ Compound Interest = Rs.(5353.5 - 4800) = Rs. 553.5