The difference between the simple interest on a certain sum at the rate of $10 \%$ per annum for $2$ years and compound interest which is compounded every $6$ months is ₹ $124.05$ . What is the principal (In ₹) ?

The sample interest on a sum of money for $3$ years is ₹ $240$ and the compound interest on the same sum, at the same rate for $2$ years is ₹ $170 .$ The rate of interest is (In $\%$)

The value of a machine depreciates at the rate of $12$ $per$ $cent$ per annum. It was purchased $3$ $years$ ago. Its present value is $Rs. 29644.032$, what was the purchase price (In $Rs.$) of the machine?

If $Rs. 1200$ amounts to $Rs. 1323$ in $2$ years at compound interest compounded annually, what will $Rs. 1600$ amount (In $Rs.$) to in $3$ years at the same rate?

If a sum of money at compound interest amounts to thrice itself in $3$ years, then in how many years will it be $9$ times itself?

If $Rs. 3000$ amounts to $Rs. 4320$ at compound interest in a certain time, then $Rs. 3000$ amount to what in half of the time (In $Rs.$) ?