The compound interest (compounding half yearly) received on Rs. 1000 for 2 years is Rs. 464.1 What is the rate of interest per annum?

Correct option is A

Given:
Principal = Rs. 1000
Time = 2 years
Rate of interest = 10%
Formula Used:
​$$C.I = P × [(1 + \frac{r}{100})^t – 1]$$​​
Here,

P = Principal Amount
r = Rate of interest
t = Time in years
Solution:
We know that -
​$$C.I = P × [(1 + \frac{r}{100})^t – 1]$$​
As,  time 2 year (half yearly) became 4 times in compounding terms
According to the question,​​
=> 464.1 = 1000 × $$[(1 + \frac{r}{100})^4 – 1]$$

​$$\frac{464.1}{1000} +1 = \left( 1 + \frac{r}{100} \right)^4\\\ \\\frac{1464.1}{1000} = \left( 1 + \frac{r}{100} \right)^4 \\ \ \\\frac{14641}{10000} = \left( 1 + \frac{r}{100} \right)^4 \\\ \\\left( \frac{11}{10} \right)^4 = \left( 1 + \frac{r}{100} \right)^4 \\\ \\\frac{11}{10} = 1 + \frac{r}{100}\\r = 10\% \text{ (compounding half yearly)} \\r = 2 \times 10 = 20\% \text{ yearly.} \\$$​​