Question

David opened a Recurring Deposit Account in a bank and deposited $₹300$ per month for $2$ yr. If he received $₹7725$ at the time of maturity, then find the rate of interest per annum.

Answer 1

Step 1: Given Data

The amount of money deposited per month, $P=₹300$,

The number of months, $$\begin{gathered} n=2\times 12 \\ =24\text{months} \end{gathered}$$

The maturity value is $₹7725$

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

The rate of interest is given by, $r$.

Step 2: Calculate the rate of interest.

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

$$\begin{gathered} 7725=\left(300\times 24\right)\left[1+\frac{r\left(24+1\right)}{2400}\right] \\ \Rightarrow 7725=7200\left[\frac{2400+25r}{2400}\right] \\ \Rightarrow \frac{7725\times 2400}{7200}=2400+25r \\ \Rightarrow 25r=2575-2400 \\ \Rightarrow r=\frac{175}{25} \\ \Rightarrow r=7\% \end{gathered}$$

Final answer: The rate of interest is 7% per annum of the given account.