Question

Mr. Anand opened a cumulative Deposit Account of monthly instalment $₹200$ at $9\%$ per annum simple interest. She earned a total interest of $₹1764$. How many instalments did he pay?

Answer 1

Step 1: Given data

The amount deposited by Mr. Anand per month is, $P=₹200$

The rate of interest is, $r=9\%$

Total interest amount, $I=₹1764$

The number of instalments paid is same as the time period, which is $n$ months.

Step 2: Calculate the number of instalments

The formula of the interest is given as, $\mathit{I}\mathbf{=}\frac{\mathit{P}\mathit{r}\mathit{n}\mathbf{(}\mathbf{n}\mathbf{+}\mathbf{1}\mathbf{)}}{\mathbf{2400}}$

Therefore, by the formula of the Interest, the number of instalments can be calculated as,

$$\begin{gathered} 1764=\frac{\left(200\times 9\times n\right)\left(n+1\right)}{2400} \\ \Rightarrow 4233600=1800n\left(n+1\right) \\ \Rightarrow 2352=n\left(n+1\right) \\ \Rightarrow n^2+n-2352=0 \\ \Rightarrow n=\frac{-1\pm \sqrt{9409}}{2} \\ \Rightarrow n=\frac{-1\pm 97}{2} \\ \Rightarrow n=\frac{96}{2},n=\frac{-98}{2} \\ \Rightarrow n=48\text{months} \end{gathered}$$

As the number of instalments cannot be a negative number, only the positive case is considered.

Final answer: Mr. Anand paid $48$ instalments.