In how many years will ₹ $2,000$ yield ₹ $662$ as compound interest at $10 \%$ per annum compounded annually?

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

The value of a machine depreciates at the rate of $12\%$ per annum. It was purchased $3$ years ago. Its present value is $Rs. 29644.032$. What was the purchase price (in $Rs.$) of the machine?

An amount of ₹ $8000$ was deposited at simple interest for $3$ years at $7.5$ $\%$ per annum. How much more would have been gained (in ₹) had it been deposited at the same rate per cent compound interest?

The compound interest on $₹ 1,800$ at $10 \%$ per annum for a certain period of time is $₹ 378$. Find the time in years.

$A$ sum of money at compound interest amounts in two years to Rs. $2809,$ and in three years to Rs. $2977.54.$ Find the rate of interest and the original sum.