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?
Answer & explanation
Correct answer: option 2
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.