If the difference between the simple and the compound interest earned on a sum of money at the rate of $5$ $p.c.p.a.$ for $2$ $years$ is $Rs. 16$,find the principal (in $Rs.$).

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.

The simple interest on a certain sum of money for $3$ years at $8 \%$ per annum is half the compound interest on ₹ $4000$ for $2$ years at $10 \%$ per annum. The sum placed on simple interest (in ₹) is

The difference between the compound interest and simple interest on a certain sum at $5 \%$ per annum for $2$ years is ₹ $1.50$. The sum is (in ₹):

The least number of completed years in which a sum of money put out at $20 \%$ $C.I.$ will be more than doubled is

$A$ bank offers $5 \%$ compound interest calculated on a half-yearly basis. $A$ customer deposits $Rs. 1600$ each on $1^{st}$ January and $1^{st}$ July of a year. At the end of the year,the amount (in $Rs.$) he would have gained by way of interest is: