A sum of Rs. 1.0 Lakh is invested for 1 year at an interest rate of 10% per annum compounded half-yearly. The compound interest is:

Correct option is B

Given:

Sum =  Rs. 1,00,000

Rate = 10% per annum 

Time = 1 years 

Interest is compounded half-yearly.

Formula Used :

​$$\text{Amount} = \text {Principal} \left(1 + \frac{r}{100}\right)^{t}$$​​

Solution:

P = Rs. 1,00,000, r = 10% and t = 1 years

If interest is compounded half-yearly.

R = 10/2 = 5% and Time = 1 × 2 = 2

As we know,

​$$A = P \left( 1 + \frac{r}{100} \right)^t\\\Rightarrow A = 1,00,000 \left( 1 + \frac{5}{100} \right)^2\\\Rightarrow A = 1,00,000 \times \left( \frac{21}{20} \right) \times \left( \frac{21}{20} \right)\\\Rightarrow A = Rs. 110250\\\text{CI} = A - P =110250- 100000 = 10250$$​​