Question

A Recurring Deposit Account of $₹1200$ per month has a maturity value of $₹12440$. If the rate of interest is $8\%$ and the interest is calculated at the end of every month, then find the time of this Recurring Deposit Account.

• A. $10$ months
• B. $20$ months
• C. $30$ months
• D. $50$ months

Answer 1

The correct option is A

$10$ months

Step 1: Given data:

Money deposited per month, $P=₹1200$

Rate of interest, $r\%=8\%$

Maturity value, $M=₹12440$

Step 2: Find the time period of this Recurring Deposit Account.

Let us assume the time period as $n$ months.

Using the formula, $\mathit{M}\mathbf{=}\mathbf{}\mathit{P}\mathbf{\times }\mathit{n}\mathbf{+}\frac{\mathit{P}\mathit{\times }\mathit{n}\mathit{(}\mathit{n}\mathit{+}\mathit{1}\mathit{)}\mathit{\times }\mathit{r}}{\mathit{2400}}$

$$\begin{gathered} \Rightarrow 12440=1200\times n+\frac{1200\times n\left(n+1\right)\times 8}{2400} \\ \Rightarrow 12440=1200n+\frac{1200\times n\left(n+1\right)\times 8}{2400} \\ \Rightarrow 12440=1200n+4n\left(n+1\right) \\ \Rightarrow 12440=1200n+4n^2+4n \\ \Rightarrow 12440=1204n+4n^2 \end{gathered}$$

$$\begin{gathered} \Rightarrow 4n^2+1204n-12440=0 \\ \Rightarrow n^2+301n-3110=0 \\ \Rightarrow \left(n+311\right)\left(n-10\right)=0 \\ \Rightarrow n=10or-311 \end{gathered}$$

As the number of months cannot be negative, therefore $n=10$months

Final Answer: The time of this Recurring Deposit Account is $\mathbf{10}$ months. Hence, Option A is correct.