A bank offers compound interest at the rate of 10% per annum when interest is compounded half-yearly. A customer deposits Rs. 3,200 each on 1st January and 1^st July of a year. At the end of the year, what will be the amount received by customer as interest?

Correct option is A

Given:
Rate of Interest = 10% per annum = 5% per half year
Deposit 1 = Rs. 3200 on 1st January (for 1 year = 2 half years)
Deposit 2 = Rs. 3200 on 1st July (for 6 months = 1 half year)
Formula Used:
Compound Interest = Amount – Principal
​$$A = P \times \left(1 + \frac{r}{100}\right)^n$$​​
Solution:
For deposit on 1st January:

$$\text{Amount} = 3200 \times \left(1 + \frac{5}{100}\right)^2 \\= 3200 \times (1.05)^2 \\= 3200 \times 1.1025 \\= 3528$$​​

For deposit on 1st July:





$$\text{Amount} = 3200 \times \left(1 + \frac{5}{100}\right)^1 \\= 3200 \times 1.05 \\= 3360$$​
Total Amount = 3528 + 3360 = 6888
Total Principal = 3200 + 3200 = 6400
Interest = 6888 – 6400 = 488