Pallavi deposited$₹46,875$ in a bank. In how many years will this sum yield a compound interest of $₹5,853$ at the rate of $8\%$ per annum compound semi-annually?

Sanju took a loan from the bank to buy a motorcycle at the rate of $15\%$ per annum compounded half-yearly. He paid a compound interest of $₹15,507$after $1\frac{1}{2}$years. Find his loan amount.

The population of a village $2$ years ago was $5,000$. If the annual growth in population during $2$ successive years was at the rate of $5\%$ and $7\%$ respectively, find the present population of the village.