Question

Ms. Mamta opened a cumulative Deposit Account of monthly instalment of $₹1200$ at $9\%$ per annum simple interest. She earned a total interest of $₹5994$ . How many instalments did she pay?

Answer 1

Given data

The amount deposited by Ms. Mamta per month is, $P=₹1200$

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

Total interest amount, $I=₹5994$

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

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, from the formula of the Interest, the number of instalments can be calculated as,

$$\begin{gathered} 5994=\frac{\left(1200\times 9\times n\right)\left(n+1\right)}{2400} \\ \Rightarrow 5994\times 2400=10800n\left(n+1\right) \\ \Rightarrow 1332=n\left(n+1\right) \\ \Rightarrow n^2+n-1332=0 \\ \Rightarrow n=\frac{-1\pm \sqrt{5328}}{2} \\ \Rightarrow n=\frac{-1\pm 73}{2} \\ \Rightarrow n=\frac{72}{2},n=\frac{-74}{2} \\ \Rightarrow n=36\text{months} \end{gathered}$$

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

Hence, Ms. Mamta paid $\mathbf{36}$ instalments.