Find the present worth of a bill of $Rs.\, 3720$ which is due for $2\, years$ at $12 \%$ compound interest,being compounded annually. (in $Rs.$)

If $Rs. 21$ is the true discount on $Rs. 371$ for a certain time,what is the true discount on the same amount for double that time,the rate being the same in both the cases? (in $Rs.$)

The banker's gain of a certain sum due $2$ $years$ hence at $12 \frac{1}{2} \%$ per annum is $Rs.\,36$. The present worth is (in $Rs.$)

$Rs. 20$ is the true discount on $Rs. 260$ due after a certain time. What will be the true discount on the same amount due after half of the earlier time,the rate of interest being the same? (in $Rs.$)

$Rs.\, 20$ is the true discount on $Rs.\, 210$ due after a certain time. What will be the true discount on the same sum due after half of the former time,the rate of interest being the same? (in $Rs.$)

The difference between the simple interest and the true discount on a certain sum of money for $2$ years at $15 \%$ per annum at simple interest is $Rs. 45$. Find the sum (in $Rs.$).