A bank offers 5% compound interest per half year. A customer deposits Rs. 6400 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:

Let's calculate the interest accumulated step by step over two half-years.
Rate of interest per half year =5%

First deposit on 1st January: Rs. 6400
This deposit earns interest for 2 half-years (until the end of the year).

Amount from 1st deposit=6400×(1+
100
5
​
)
2

Amount=6400×(1.05)
2
=6400×1.1025=Rs. 7056
Interest from 1st deposit=7056−6400=Rs. 656
Second deposit on 1st July: Rs. 6400
This deposit earns interest for 1 half-year (until the end of the year).

Amount from 2nd deposit=6400×(1+
100
5
​
)
1

Amount=6400×1.05=Rs. 6720
Interest from 2nd deposit=6720−6400=Rs. 320
Total interest gained:

Total Interest=656+320=Rs. 976