A sum of money at compound interest becomes $$\frac{3}{2}$$times of itself in 2 years. In how many years will it become $$\frac{81}{16}$$ times of itself, interest compounded annually?

The question had an error in the original questions paper the fraction $$\frac{81}{16}$$ was given as $$\frac{18}{16}$$.

Taking the multiplication factor of this compound interest to be X and the principal amount be P.
We are given that 
$$P\left(X\right)^2=\frac{3}{2}P$$
which would give us, $$X=\ \left(\frac{3}{2}\right)^{\frac{1}{2}}$$

Using this for the second condition we had, 
we can get 
$$P\left(X\right)^N\ =\ \frac{81}{16}P$$
$$\left(\frac{3}{2}\right)^{N\times\ \frac{1}{2}}\ =\ \frac{81}{16}$$
$$\left(\frac{3}{2}\right)^{N\times\ \frac{1}{2}}\ =\ \left(\frac{3}{2}\right)^4$$
Giving us N=8.

Therefore, Option B is the correct answer.