The sum for $2$ years gives a compound interest of ₹ $3225$ at the rate of $15 \%$ per annum. The principal amount is (in ₹):

The compound interest on a certain sum of money for $2$ years at $5 \%$ per annum is ₹ $410$. The simple interest (in ₹) on the same sum at the same rate and for the same time is:

$A$ certain sum of money at compound interest grows up to ₹ $12960$ in $2$ years and up to ₹ $13176$ in $3$ years. Find the rate per cent per annum.

There is a $60 \%$ increase in an amount in $6$ years at simple interest. What will be the compound interest (in ₹) of ₹ $12000$ after $3$ years at the same rate?

Which of the statements given below are sufficient to answer the following question?
What is the rate of interest per annum on an investment of $Rs. 800$?
$(I)$ The income from $S.I.$ at the end of $3$ years at the same rate of interest is $19$.
$(II)$ $C.I.$ is $15.76$ more than $S.I.$ on the same sum and same rate in $2$ years.

$A$ certain sum of money invested at compound interest becomes $1.44$ times of itself in $2$ years. If twice this sum were lent at simple interest, in how many years would it double itself?