Question

Mohan has a Recurring Deposit Account in a bank for $2$ yr at $6\%$ per annum simple interest. If he gets $₹1200$ as interest at the time of maturity, then find

1. the monthly instalment.
2. the amount of maturity.

Answer 1

Step 1: Given data:

Time period, $$\begin{gathered} n=2\times 12 \\ =24\text{months} \end{gathered}$$

Interest on maturity $=₹1200$

The rate of interest is given by, $r=6\%$

Step 2: Write the given data and calculate the value of the monthly instalment:

Consider the amount deposited per month, which is same as the value of the monthly instalment, as $P$.

The formula for the interest $=\frac{\mathbf{P}\mathbf{r}\mathbf{n}\mathbf{(}\mathbf{n}\mathbf{+}\mathbf{1}\mathbf{)}}{\mathbf{2400}}$

Therefore, from the formula of the interest, the value of the monthly instalment be calculated as,

$$\begin{gathered} 1200=\frac{\left(P\times 6\times 24\right)\left(24+1\right)}{2400} \\ \Rightarrow 1200=\frac{3600}{2400}P \\ \Rightarrow P=\frac{1200\times 2400}{3600} \\ \Rightarrow P=₹800 \end{gathered}$$

Step 3: Calculate the maturity amount:

The formula of the maturity value is, $\mathit{P}\mathbf{\times }\mathit{n}\mathbf{+}\mathbf{\text{Interest}}$.

Therefore, the maturity value is:

$$\begin{gathered} \left(800\times 24\right)+1200 \\ =19200+1200 \\ =₹20400 \end{gathered}$$

Final answer: Hence, the monthly instalment amount is $₹800$ and the maturity amount is $₹20400$.