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?

$A$ sum of money placed at compound interest doubles itself in $4$ $years$. In how many $years$ will it amount to four times itself?

₹ $3757$ is to be divided between $A$ and $B$ such that $A$'s share at the end of $7$ years may be equal to $B$'s share at the end of $9$ years. If the rate of interest is $10 \%$ per annum compounded annually,what is $B$'s share (in ₹)?

Find the compound interest on $Rs. 32000$ at $20 \%$ per annum for $1$ year,compounded half-yearly (in $Rs.$).

Monica deposited a total of $Rs. 10500$ with a bank in two different deposit schemes at $10 \%$ $p.a.$,interest being compounded annually. As per the schemes,she gets the same amount after $2 \,years$ on the first deposit as she gets after $3 \,years$ on the second deposit. How much money (In $Rs.$) did she deposit for $3 \,years$?

$A$ 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.