A sum of money amounts to $₹13,230$ in one year and $₹13,891.50$ in $1\frac{1}{2}$ years at compound interest compounded semi-annually. Find the sum and the rate of interest per annum.

The SI and CI on a sum of money for $2$ years are $200$and $210$, respectively. If the rate of interest is same, find the sum and the rate.

$24,000$ blood donors were registered with a charitable hospital. The number of donors increased at the rate of $5\%$ every six months. Find the time period at the end of which the total number of blood donors would become $27783$.
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Narendra makes a fixed deposit of $₹1,60,000$ for $2$ years in a bank. If the bank pays interest at the rate of $10\%$ per annum compounded half-yearly, how much will Narendra get back at the time of maturity?

Provide $₹1,95,150$ between $A$ and $B$ so that the amount that $A$ receives in $2$ years is the same as that $B$ receives in $4$ years. The interest is compounded annually at the rate of $4\%$ per annum.

Find the compound interest on $₹25,000$ at $12\%$ per annum for $2\frac{1}{2}$ years, compounded annually.

On a certain sum, borrowed at $10\%$ per annum for $1$ year, the difference between the compound interest reckoned half-yearly and that reckoned quarterly is $₹33.61$. Calculate the sum.