A bank pays compound interest at the rate of 5% per annum, compounding half-yearly. A customer deposited Rs.1,600 each on 1 January and 1 July of a year. The interest he would get on the sum deposited at the end of the year is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. Rs. 121.
Given that
The rate of compound interest is 5% p.a.
If compounded half-yearly, rate of interest = 5/2 = 2.5%
Therefore, two times interest will be added to the amount deposited on 1st January and one time interest will be added to the amount deposited on 1st July.
The principal amount is Rs. 1600 each on 1st January and 1st July of year
As we know,
Amount = Principal (1 + rate/100)time
Therefore, total amount at the end of one year on the money deposited on 1st January and 1st July is,
⇒ मिश्रधन = 1600 (1 + 2.5/100)2 + 1600 (1 + 2.5/100)1
⇒ मिश्रधन = 1600 (41/40)2 + 1600 (41/40)
⇒ मिश्रधन = 1600 × 1681/1600 + 80 × 21
⇒ मिश्रधन = 1681 +1640 = 3321 रुपये
The total principal amount deposited in a year is 1600 + 1600 = 3200
The total amount gained in a year = 3321
Hence, the interest gained is 3321 - 3200 = Rs. 121