If ₹ $\; 15,000$ is earned as interest on a monthly deposit of ₹ $\; 5,000$ for $2$ years. Find the rate of interest on the recurring deposit.
Money deposited each month $= P =$ ₹ $5,000$
Time for which money deposited $= n = 2 $ years $= 24 $ months
Let, rate of interest $= r \%$
Interest received $= $ ₹ $15,000$
$\text{Interest} = P \times \dfrac{n \left(n + 1\right)}{2 \times 12} \times \dfrac{r}{100}$
i.e. $\;$ $15000 = 5000 \times \dfrac{24 \times 25}{2 \times 12} \times \dfrac{r}{100}$
i.e. $r = \dfrac{15000 \times 2 \times 12 \times 100}{5000 \times 24 \times 25} = 12 \%$
$\therefore \;$ Rate of interest on the recurring deposit $= 12 \%$