Question

Mr. Richard has a Recurring Deposit Account in a bank for $3$ yr at $7.5\%$ per annum simple interest. If he gets $₹8325$ as interest at the time of maturity, then find

1. the monthly deposit.
2. the maturity value.

Answer 1

Step 1: Write the given data and calculate the value of monthly instalment

Consider the amount deposited per month, as $P$

Time period, $$\begin{gathered} n=3\times 12 \\ =36\text{months} \end{gathered}$$

Interest on maturity $=₹8325$

The rate of interest is given by, $r=7.5\%$

The formula for the interest is given by: $\frac{\mathbf{P}\mathbf{r}\mathbf{n}\left(n+1\right)}{\mathbf{2400}}$

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

$$\begin{gathered} 8325=\frac{\left(P\times 7.5\times 36\right)\left(36+1\right)}{2400} \\ \Rightarrow 8325=\frac{9990}{2400}P \\ \Rightarrow P=\frac{8325\times 2400}{9990} \\ \Rightarrow P=₹2000 \end{gathered}$$

Step 2: 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:

$$\begin{gathered} 36P+8325 \\ =\left(2000\times 36\right)+8325 \\ =72000+8325 \\ =₹80325 \end{gathered}$$

Final answer:

The monthly instalment amount is $₹2000$ and the maturity amount is $₹80325$.