Question

Ms. Vasundhra Mehta has a recurring deposit account in a bank for 4 years at 10% p.a. She gets Rs. 6370 as the interest on maturity. Find:

(i) the monthly instalment.

(ii) the maturity value.​

Answer 1

Step 1: Given data:

Interest received on maturity, $\left(I\right)=\mathrm{Rs}.6370$

Rate of Interest, $\left(R\right)=10\%\mathrm{p}.\mathrm{a}.$

Number of years, $\left(n\right)=4$

Convert years into months.

$$\begin{gathered} n=4 \\ =4\times 12\left(\because 1\mathrm{year}=12\mathrm{months}\right) \\ =48 \\ \mathrm{So},n=48\mathrm{months} \end{gathered}$$

Step 2: Calculate the monthly instalment:

Let the monthly instalment be $\mathrm{Rs}.P$.

Then,

$\begin{array}{rcl}\mathrm{Interest}\mathrm{recieved}& =& P\times \frac{n\left(n+1\right)}{2\times 12}\times \frac{R}{100}\\ & \Rightarrow & 6370=P\times \frac{48\left(48+1\right)}{2\times 12}\times \frac{10}{100}\\ & \Rightarrow & 6370=P\times \frac{48\times 49}{2\times 12}\times \frac{10}{100}\\ & \Rightarrow & 6370=P\times \frac{48\times 49}{2\times 12}\times \frac{1}{10}\\ & \Rightarrow & 6370=P\times \frac{49}{5}\\ & \Rightarrow & P=\frac{6370\times 5}{49}\\ \therefore P& =& \mathrm{Rs}.650\end{array}$

Hence, the monthly instalment is $\mathrm{Rs}.650$.

Step 3: Calculate the maturity value:

$\begin{array}{rcl}\mathrm{Maturity}\mathrm{value}& =& \mathit{[}1\mathit{+}\frac{\left(n\mathit{+}\mathit{1}\right)R}{2400}\mathit{]}\times n\times P\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{=}& [1+\frac{\left(48+1\right)\times 10}{2400}]\times 48\times 650\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{=}& [1+\frac{49\times 10}{2400}]\times 48\times 650\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{=}& [1+\frac{490}{2400}]\times 48\times 650\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{=}& [1+\frac{490}{2400}]\times 31200\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{=}& \left[\frac{2400+490}{2400}\right]\times 31200\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{=}& \left[\frac{2890}{2400}\right]\times 31200\\ & =& 37570\\ \therefore \mathrm{Maturity}\mathrm{value}& =& \mathrm{Rs}.37570\end{array}$

Hence, the monthly instalment is $\mathrm{Rs}.650$ and the maturity value is $\mathrm{Rs}.37570$.