A sum of money doubles itself at a compound interest in 8 years. In how many years will it become four times itself?

Correct option is D

Given:

The sum of money doubles in 8 years at compound interest.

We need to find how many years it will take for the sum to become four times itself.

Formula Used:

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

Solution:

Where:

A = final amount

P = principal

r = rate of interest

t = time in years

​$$2P = P \left(1 + \frac{r}{100}\right)^8$$​

​$$2 = \left(1 + \frac{r}{100}\right)^8$$  

​​$$\left(1 + \frac{r}{100}\right) = 2^{\frac{1}{8}}$$  ..........equation (!)​

$$4P = P \left(1 + \frac{r}{100}\right)^t$$​

4 = $$\left(1 + \frac{r}{100}\right)^t$$ ............equation 

4 = $$\left(2^{\frac{1}{8}}\right)^t$$​​

4 = $$2^{\frac{t}{8}}$$​

2 = $$\frac{t}{8}$$​

t = 16 years