A bank offers $10\%$ compound interest per half year. A customer deposits $\text{Rs }3600$ each on $1^{\text{st}}\text{ January}$ and $1^{\text{st}}\text{ July}$ of a year. At the end of the year, the amount he would have gained by way of interest is:

The interest is compounded half-yearly at a rate of $10\%$ per half-year.For the deposit made on $1^{\text{st}}\text{ January}$:This amount remains in the bank for two half-year periods.
$$\text{Amount after 1 year}=3600\times {\left(1+\frac{10}{100}\right)}^2=3600\times (1.1{)}^2=3600\times 1.21=\text{Rs }4356$$
$$\text{Interest gained}=4356-3600=\text{Rs }756$$
For the deposit made on $1^{\text{st}}\text{ July}$:This amount remains in the bank for one half-year period.
$$\text{Amount after half year}=3600\times \left(1+\frac{10}{100}\right)=3600\times 1.1=\text{Rs }3960$$
$$\text{Interest gained}=3960-3600=\text{Rs }3600\times 0.10=\text{Rs }360$$
Total Interest Gained:
$$\text{Total Interest}=756+360=\text{Rs }1116$$