Shahrukh opened a Recurring Deposit Account in a bank and deposited ₹800 per month for 1½ years. If he received ₹15084 at the time of maturity, find the rate of interest per annum.

Here,
P = money deposited per month = ₹800,
n = number of months for which the money is deposited = 1 x 12 + 6 = 18

Let the rate of interest be r% per annum, then by using the formula:

$I = P \times \dfrac{n(n+1)}{2 \times 12} \times \dfrac{r}{100} \text{, we get} \\[0.7em] I = \Big( 800 \times \dfrac{18 \times 19}{2 \times 12} \times \dfrac{r}{100} \Big) \\[0.5em] \enspace\medspace = 114r$

Total money deposited by Shahrukh = ₹800 x 18 = ₹14400

∴ The amount of maturity = total money deposited + interest
= 14400 + 114r

According to the given,

$14400 + 114r = 15084 \\[0.5em] \Rightarrow 114r = 15084 - 14400 \\[0.5em] \Rightarrow 114r = 684 \\[0.5em] \Rightarrow r = \dfrac{684}{114} \\[0.5em] \Rightarrow r = 6$

∴ Rate of (simple) interest = 6% p.a.