How long will it take a sum of money invested at 6% p.a. on simple interest to increase its value by 50%?

Correct option is B

Given:

Rate of interest (R) = 6% per annum

Increase in value = 50% of the principal (P)

We need to find the time (T)

Formula Used:

​$$SI = \frac{P \times R \times T}{100}$$​​

Solution:

Since the increase in value is 50% of P, we have:

​$$SI = \frac{50}{100}P = 0.5P$$​​

​$$0.5P = \frac{P \times 6 \times T}{100}$$​​

0.5 =$$\frac{6T}{100}$$​​

T =$$\frac{0.5 \times 100}{6}$$​​

T =$$\frac{50}{6}$$=​8$$\frac{1}{3}$$ ​ years​

Option (B) is right.