Question

Shahrukh opened a Recurring Deposit Account in a bank and deposited $₹800$ per month for $1\frac{1}{2}$ yr. If he received $₹15084$ at the time of maturity, then find the rate of interest per annum.

Answer 1

Step 1: Write the given data

The amount deposited by Shahrukh per month is, $P=₹800$

Time period, $$\begin{gathered} n=1\frac{1}{2}\times 12 \\ =18\text{months} \end{gathered}$$

Maturity value $=₹15084$

Consider, the rate of interest as $r\%$ per annum.

Step 2: Calculate the rate of interest per annum

The Maturity value is given by: $\left(P\times n\right)\left[1+\frac{r(n+1)}{2400}\right]$

Therefore, by the formula of the Maturity value, the rate of interest can be calculated as,

$$\begin{gathered} 15084=\left(800\times 18\right)\left[1+\frac{r\left(18+1\right)}{2400}\right] \\ \Rightarrow 15084=14400\left[\frac{2400+19r}{2400}\right] \\ \Rightarrow \frac{15084\times 2400}{14400}=2400+19r \\ \Rightarrow 19r=2514-2400 \\ \Rightarrow r=\frac{114}{19} \\ \Rightarrow r=6\% \end{gathered}$$

Final answer: The rate of interest per annum is $6\%$.