A certain sum of money amounts to 3 times of itself in 13 years when interest is compounded annually at a certain rate of interest per annum. In how many years will the initial sum amount to 9 times of itself at the same rate of interest per annum, also compounded annually?
Answer & explanation
Correct answer: option 2
Sum amounts to three times of itself in 13 years,
ATQ,
Amount = P$(1 \;+\; \frac{R}{100})^t$
3P = P[ 1 + \(\frac{R}{100}\) ]¹³
3 = [ 1 + \(\frac{R}{100}\) ]¹³
On squaring both side ,
3² = { [ 1 + \(\frac{R}{100}\) ]¹³ }²
9 = [ 1 + \(\frac{R}{100}\) ]26
So, sum become 9 times of itself in 26 years.