In what duration will a sum of money double itself at 10% per annum rate of simple interest?

Correct option is A

Given:

Rate of interest (r) = 10% 

Amount = 2× Principal 

Formula Used:

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

Where:

A is the final amount (which will be double the principal),

P is the principal amount (the initial sum of money),

r is the rate of interest per annum,

t is the time in years.

Solution:  

According to the question;

​$A=2P$

​Substitute $A=2P$ and $r=10$ into the formula:

​$$2P = P \left( 1 + \frac{10t}{100} \right)$$ 

$$2P = P \left( 1 + 0.1t \right)$$ 

​$$2 = 1 + 0.1t$$​​

$$2−1=0.1t$$​​

 $$1=0.1t$$​​

 $$t = \frac{1}{0.1} = 10 \, \text{years}$$​​

 Thus, the sum of money will double in 10 years at an interest rate of 10% per annum under simple interest.​