A sum of money placed at compound interest doubles itself in $5$ years. In how many years would it be $8$ times of itself at the same rate of interest?

Under compound interest, if a sum becomes $2$ times ($2^1$) in $5$ years, then it increases exponentially by powers of $2$:
* Becomes $2^1=2$ times in $1\times 5=5$ years.
* Becomes $2^2=4$ times in $2\times 5=10$ years.
* Becomes $2^3=8$ times in $3\times 5=15$ years.

Thus, it will become $8$ times itself in $15$ years.