A sum of money earns simple interest equal to 0.5 times the sum in 10 years; the rate of interest per annum is :

1. 20%

2. 10%

3. 5%

4. none of these

Given:

S.I. = 0.5P

= $\dfrac{5}{10}$ P

T = 10 years

Let the rate be $r$.

We know,

$\text{S.I.} = ₹ \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \dfrac{5}{10}P = ₹ \Big(\dfrac{P \times r \times 10}{100}\Big)\\[1em] \Rightarrow \dfrac{1}{2} \cancel{P} = ₹ \dfrac{\cancel{P} \times R \times 10}{100}\\[1em] \Rightarrow \dfrac{1}{2} = ₹ \dfrac{R}{10}\\[1em] \Rightarrow R = \dfrac{10}{2}\\[1em] \Rightarrow R = 5$

Hence, option 3 is the correct option.