A bank offers 15% compound interest per half year. 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:

The rate of interest is 15% per half-year.
For the first deposit (Rs 2400 on 1st January):
This amount stays in the bank for the full year, which means 2 half-yearly cycles.

Amount
1
​
=P(1+
100
R
​
)
2
=2400(1+
100
15
​
)
2

Amount
1
​
=2400×(1.15)
2
=2400×1.3225=Rs 3174
For the second deposit (Rs 2400 on 1st July):
This amount stays in the bank for 6 months, which means 1 half-yearly cycle.

Amount
2
​
=P(1+
100
R
​
)
1
=2400(1+
100
15
​
)
Amount
2
​
=2400×1.15=Rs 2760
Total Amount at the end of the year:

Total Amount=Amount
1
​
+Amount
2
​
=3174+2760=Rs 5934
Total Principal Deposited:

Total Principal=2400+2400=Rs 4800
Total Interest Gained:

Interest=Total Amount−Total Principal=5934−4800=Rs 1134