The population of a state increases by $10 \%$ every year. If its population in the year $2003$ was $15$ lakhs, what was its population in the year $2005$ (in $lakhs$)?

A sum of money lent at compound interest for $2 \,yr$ at $20 \%$ pa would fetch $Rs. 964$ more, if the interest was payable half-yearly than if it was payable annually. What is the sum (In $Rs.$) ?

The difference between the simple and compound interest on a certain sum of money for $2$ years at $4 \%$ per annum is $Rs. 4$. Find the sum (In $Rs.$) ?

The difference between $C.I.$ & $S.I.$ on $Rs. 700$ in $2$ years at $5 \%$ per annum is (In $Rs.$)

Rohit invested some amount at the rate of $6$ per cent pa and at the end of $3$ years he got ₹ $8730$ simple interest. How much compound interest (in ₹) he will get on same amount and same rate of interest after $2$ years.

Sonika invested an amount of ₹ $5800$ for $2$ years. At what rate of compound interest ($\%$ $per$ $annum$) will she get an amount of ₹ $594.5$ at the end of two years?