A sum doubles in 4 years at a certain rate of compound interest. In how many years does it amount to 8 times itself at the same rate?

12

The Formula that we used here is -

Amount = P$(1 \;+\; \frac{R}{100})^t$

2P = P[ 1 +  \(\frac{R}{100}\) ]⁴

2 = [ 1 +  \(\frac{R}{100}\) ]^{4     -----(1)}

ATQ,

8P = P[ 1 +  \(\frac{R}{100}\) ]^t

2³ = [ 1 +  \(\frac{R}{100}\) ]^{t   ----(2)}

On cubing equation 1,

2³ = [ (1 +  \(\frac{R}{100}\) )4 ]³

2³ = [ 1 +  \(\frac{R}{100}\) ]¹²    ----(3)

On comparing equation 3 with equation 1.

t = 12 years

So, After 12 years , the sum becomes 8 times of itself.