What sum will give ₹ $244$ as the difference between simple interest and compound interest at $10 \%$ per annum in $1 \frac{1}{2}$ years,compounded half-yearly?

$A$ sum of ₹ $15000$ deposited at compound interest becomes double after $5$ $years$. After $20$ $years$,it will become (in ₹):

The simple interest accrued on an amount of $Rs. 19800$ at the end of $3$ years is $Rs. 7128$. What would be the compound interest (in $Rs.$) accrued on the same amount at the same rate in the same period?

In what time (in $years$) will ₹ $8,000$ at $3 \%$ per annum produce the same interest as ₹ $6,000$ does in $5$ years at $4 \%$ simple interest?

Sita deposited $Rs. 5000$ at $10\%$ simple interest for $2$ years. How much more money (in $Rs.$) will Sita have in her account at the end of $2$ years,if it is compounded semi-annually?

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?