A sum of 400 would become Rs. 441 after 2 years at r% p.a. compound interest. Find the value of r.

Correct option is B

Given:

A sum of 400 would become Rs. 441

time =2 years

Formula used: 

​$$A = P \left(1 + \frac{r}{100}\right)^t$$ 

solution;

​$$441 = 400 \left(1 + \frac{r}{100}\right)^2 \\\frac{441}{400} = \left(1 + \frac{r}{100}\right)^2 \\\frac{441}{400} = \left(\frac{21}{20}\right)^2 \\\left(1 + \frac{r}{100}\right) = \frac{21}{20} \\1 + \frac{r}{100} = \frac{21}{20} \\\frac{r}{100} = \frac{21}{20} - 1 \\\frac{r}{100} = \frac{1}{20} \\r = \frac{100}{20} = 5$$

so rate is =5%