On a certain principal,if the simple interest for two years is ₹ $1400$ and the compound interest for two years is ₹ $1449$,what is the rate of interest (in $\%$) ?

If the difference between the compound interest and simple interest on a sum of money for $3$ years is ₹ $186$,find the sum of money (in ₹) if the rate of interest in both cases is $10 \%$.

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?

$A$ certain sum of money at compound interest grows up to ₹ $12960$ in $2$ years and up to ₹ $13176$ in $3$ years. Find the rate per cent per annum.

The difference between the compound and simple interest on a sum of money for $2$ years at $6 \frac{1}{4} \%$ per annum is $Rs. 10$. The sum (in $Rs.$) is

$A$ man borrows ₹ $3825$ to be paid back with compound interest at the rate of $4 \%$ per annum by the end of $2$ years in two equal yearly instalments. How much will be each instalment (in ₹)?