David opened a Recurring Deposit Account in a bank and deposited ₹ 300 per month for two years. If he received ₹ 7725 at the time of maturity, find rate of interest per annum.

Let rate of interest given by bank = x%.

So,

P = ₹ 300, n = (2 × 12) = 24 months and r = x%

I = $P \times \dfrac{n(n + 1)}{2 \times 12} \times \dfrac{r}{100}$

$\therefore I = ₹ 300 \times \dfrac{24 \times 25}{2 \times 12} \times \dfrac{x}{100} \\[1em] = ₹ 300 \times \dfrac{x}{4} \\[1em] = ₹ 75x$

Maturity value = Sum deposited + Interest

= $₹ 300 \times 24 + ₹ 75x = ₹ 7200 + ₹ 75x$

Given, maturity value = ₹ 7725.

$\therefore 7200 + 75x = 7725 \\[1em] \Rightarrow 75x = 525 \\[1em] \Rightarrow x = \dfrac{525}{75} = 7.$

Hence, the rate of interest given by bank is 7%.