Question

A sum of money becomes 5/4 times of itself in 4 years at a certain rate of simple interest. The rate per annum is:

Answer 1

let sum be x
amount = 5x/4
si = 5x/4-x = x/4
rate = x×100/4×x×4
25/4%

Answer 2

The rate of interest per annum is 25%.

Step-by-step explanation:

Let the principal is P and the final value is $\frac{5P}{4}$.

If the simple interest is r%, then after 4 years, the principal P becomes $\frac{5P}{4}$.

Therefore, we can write the equation as

$\frac{5P}{4} = P(1 + \frac{4r}{100} )$

⇒ $(1 + \frac{r}{100}) = 1.25$

⇒ $\frac{r}{100} = 0.25$

⇒ r = 25%

Therefore, the rate of interest per annum is 25%. (Answer)