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?

26 years

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.