$A$ certain sum will amount to ₹ $12,100$ in $2$ years at $10 \%$ per annum of compound interest,interest being compounded annually. The sum is (In ₹)

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 $2010$?

Find the least number of complete years in which a sum of money put out at $20 \%$ compound interest will be more than double?

What is the rate of interest (in $\%$) if simple interest earned on a certain sum for the $3^{rd}$ year is $₹ 2,000$ and compound interest earned in $2$ years is $₹ 4,160$?

Suneeta borrowed a certain sum from Reena for $2 \,yr$ at simple interest. Suneeta lent this sum to Venu at the same rate for $2 \,yr$ at compound interest. At the end of $2 \,yr$,she received $Rs. 110$ as compound interest but paid $Rs. 100$ as simple interest. Find the sum and the rate of interest.

How many statements are required to find the rate of interest percent $p.a.$?
$Statements:$
$I$. The difference between the compound interest and simple interest earned in two years on the amount invested is ₹ $100$.
$II$. The amount becomes ₹ $19,500$ in three years on simple interest.
$III$. The simple interest accrued in two years on the same amount at the same rate of interest is ₹ $3,000$.