What is rate of compound interest if sum becomes $$\frac{1331}{729}$$​ of itself  in 3 years?

Correct option is C

Given:

Amount becomes$$\frac{1331}{729}$$​​

Time =3 years

Formula Used:

Compounded Amount =$$Principle \times \left(1+ \frac{r}{100}\right)^{t}$$​​

Amount = Principle + Interest

Solution:

Let Principle be P

Amount $$=\frac{1331}{729} \times P$$​

​$$\frac{1331}{729} \times P = P \left(1+ \frac{r}{100}\right)^{3}$$​​

​$$\left(\frac{11}{9}\right)^3 = \left(1+ \frac{r}{100}\right)^{3}$$​​

​$$\frac{11}{9} = 1+ \frac{r}{100}$$​​

​$$\frac{11}{9} -1 = \frac{r}{100}$$​​

​$$\frac{11-9}{9} = \frac{r}{100}$$​​

​$$\frac{2}{9} = \frac{r}{100}$$​​

​$$r =\frac{200}{9} = 22\frac{2}{9}\%$$ 

thus, the rate of interest is $$22\frac{2}{9}\%$$​​