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 ₹):

$A$ man borrows $Rs. 5100$ to be paid back with compound interest at the rate of $4 \%$ p.a. by the end of $2$ years in two equal yearly instalments. How much (in $Rs.$) will be each instalment?

What will be the compound interest on a sum of ₹ $25000$ after $3$ years at the rate of $12 \%$ per annum?

Raghu invested a certain sum in Scheme $X$ for $4$ years. Scheme $X$ offers simple interest at $12\%$ per annum for the first two years and compound interest (compounded annually) at $20\%$ per annum for the next two years. The total interest earned by him after $4$ years is $₹ 11016$. What was the sum (in $₹$) invested by Raghu in Scheme $X$?

Sonika invested an amount of ₹ $5800$ for $2$ years. At what rate of compound interest ($\%$ per annum) will she get an amount of ₹ $594.5$ as interest at the end of two years?

$A$ sum of money lent at compound interest amounts to ₹ $1460$ in $2$ years and to ₹ $1606$ in $3$ years. The rate of interest (in $\%$) per annum is: