If the compound interest on a certain sum for $2$ years is ₹ $105$ and simple interest is ₹ $100$,then the sum (in ₹) is:

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:

$A$ sum of ₹ $1260$ is borrowed from a money lender at $10 \%$ p.a. compounded annually. If the amount is to be paid back in two equal annual instalments,find out the annual instalment (in ₹).

The compound interest accrued on an amount at the end of $3$ $years$ at $15$ $p.c.p.a.$ is $Rs. 6500.52$. What is the principal amount (in $Rs.$)?

In the year $2008$,$5000$ students were admitted to a college. It is found that the number of students admitted is constantly increasing by $24\%$ per year. How many students will be admitted to the college in the year $2010$?

Sonika invested an amount of ₹ $5800$ for $2$ years. At what rate of compound interest (in $\% \text{ p.a.}$) will she get an amount of ₹ $594.50$ as interest at the end of two years?