What sum of money (in $Rs.$) at compound interest will amount to $Rs. 5305.53$ in $3$ years,if the rate of interest is $1 \%$ for the first year,$2 \%$ for the second year,and $3 \%$ for the third year?

On a certain sum of money,the simple interest for $2$ years is ₹ $200$ at the rate of $7 \%$ per annum. Find the difference between compound interest $(CI)$ and simple interest $(SI)$. (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?

$A$ man gets a simple interest of $Rs. 1000$ on a certain principal at the rate of $5$ $p.c.p.a.$ in $4$ years. What compound interest (in $Rs.$) will the man get on twice the principal in two years at the same rate?

The population of a state increases by $10 \%$ every year. If its population in the year $2003$ was $15$ lakhs,what was its population in the year $2005$ (in lakhs)?

$B$ borrows ₹ $5,000$ from $A$ at $6 \%$ p.a. simple interest and lends it to $C$ at compound interest of $10 \%$ p.a. If $B$ collects the money back from $C$ after $2$ years and repays $A$,the profit made by $B$ in the transaction is (in ₹):