The difference between simple and compound interest on a sum of $10000$ is $64$ for $2$ years. Find the rate of interest. (in $\%$)

$A$ certain sum at compound interest amounts in two years to ₹ $2809$ and in three years to ₹ $2977.54$. Find the rate of interest and the original sum (in ₹).

Find the difference between $S.I.$ and $C.I.$ (in $Rs.$) at $14 \%$ per annum for $2$ years on a principal of $Rs. 10000$.

What will be the difference between simple and compound interest (in ₹) at $10 \%$ per annum on a sum of ₹ $1000$ after $4$ years?

What is $C.I.$ (in $Rs.$) on $Rs. 7500$ for $4$ years if the rate of interest is $10 \%$ p.a. for the first $2$ years and $20 \%$ p.a. for the next $2$ years?

The simple and compound interests on a sum of money for $2$ years are ₹ $8400$ and ₹ $8652$ respectively. The rate of interest per annum is (in $\%$):