At what rate per cent of simple interest does a sum of money double itself in 12 years?

Correct option is C

Given:

The sum of money doubles, so A=2P (i.e., the final amount is twice the principal).

The time (t)=12 years.

Formula Used:

The formula for calculating the amount A using simple interest is:

​$$A = P + \frac{P \times r \times t}{100}$$ 

Where:

A = Final amount (Principal + Interest)

P = Principal (Initial sum of money)

r = Rate of interest per annum (in percentage)

t = Time in years

Solution:

Since the amount doubles, we know:

A = 2P 

Substitute into the simple interest formula:

​$$2P = P + \frac{P \times r \times 12}{100}$$ 

$$2P-P = \frac{P \times r \times 12}{100}$$ 

​$$P = \frac{P \times r \times 12}{100}$$​​

​​$$r = \frac{100}{12}$$ 

$$r = 8\frac{1}{3}$$%

Thus the rate of interest required for the sum of money to double in 12 years is 8.33% per annum.