​A sum of money becomes 8 times of itself in 3 years at compound interest compounded annually. The rate of interest is: _____________​

Correct option is A

Given:

A sum of money becomes 8 times of itself in 3 years at compound interest compounded annually

Final amount (A) = 8 times the principal (8P)

Formula used:

The compound interest formula is

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

Solution:

​$$8P = P \left(1 + \frac{r}{100}\right)^3$$​​

​$$8 = \left(1 + \frac{r}{100}\right)^3$$

​​Take the cube root of both sides: 

​$$2 = 1 + \frac{r}{100}$$ 

​$$1 = \frac{r}{100}$$ 

r = 100 

So, the rate of interest is 100% per year​