A sum of money at compound interest doubles itself in 15 years. It will become eight times of itself in?

Let's assume sum of money to be $$x$$ and rate of compound interest is $$r$$
hence $$x\times(1+\frac{r}{100})^{15}$$ = $$2x$$
or $$(1+\frac{r}{100})^{15}$$ = 2
$$(1+\frac{r}{100})$$ = $$2^{\frac{1}{15}}$$
now we have to find time in which it got 8 times, let's say it is n
hence $$x\times(1+\frac{r}{100})^{n}$$ = $$8x$$
or $$(1+\frac{r}{100})^{n}$$ = $$8$$
or $$2^{\frac{n}{15}}$$ = $$2^{3}$$
we get n = 45