The amount of money needed to ensure for a prize of ₹ 5000 at the begining of each year indefinitely if money is worth 5% compounded annually is:

The prize of ₹5000 is paid at the beginning of each year, indefinitely. This is a perpetuity due problem where payments occur at the start of each period.

For a perpetuity due, the present value formula is:

$\text{Present Value} = \text{Payment} \times \frac{(1 + r)}{r}$

Where:

Payment = ₹5000

$r = 5\% = 0.05$

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$PV = 5000 \times \frac{(1 + 0.05)}{0.05}$

$PV = 5000 \times \frac{1.05}{0.05}$

$PV = 5000 \times 21$

$PV = ₹1,05,000$

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The formula uses $\frac{(1+r)}{r}$ instead of $\frac{1}{r}$ because the first payment occurs immediately (at the beginning of the year), requiring additional funds upfront.

For payments at the end of each period, the formula would be $\frac{\text{Payment}}{r}$.

For payments at the beginning of each period, the formula is $\text{Payment} \times \frac{(1+r)}{r}$.

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Therefore, the amount needed is ₹1,05,000.