Question

David opened a recurring deposit account in a bank and deposited $\mathrm{Rs}.300$ per month for two years. If he received $\mathrm{Rs}.7725$ at the time of maturity, find the rate of interest per annum.

Answer 1

Step 1: Given data

Installment per month, $\left(P\right)=\mathrm{Rs}.300$

Time, $n=2$ years

Maturity amount received by David$=\mathrm{Rs}.7725$

Step 2: Convert years into months

$$\begin{gathered} n=2years \\ =2\times 12\left(\because 1\mathrm{year}=12\mathrm{months}\right) \\ =24\mathrm{months} \end{gathered}$$

So, $n=24months$

Calculate the rate of Interest:

Let the Rate of interest be $R\%\mathrm{p}.\mathrm{a}.$

Then,

$$\begin{gathered} \mathrm{Maturity}\mathrm{amount}=\left[1+\frac{(n+1)R}{2400}\right]\times n\times P \\ \Rightarrow 7725=\left[1+\frac{(24+1)R}{2400}\right]\times 24\times 300 \\ \Rightarrow 7725=\left[1+\frac{25\times R}{2400}\right]\times 7200 \\ \Rightarrow 7725=\left[\frac{2400+25R}{2400}\right]\times 7200 \\ \Rightarrow \frac{7725}{7200}=\frac{2400+25R}{2400} \\ \Rightarrow 2400+25R=\frac{7725}{7200}\times 2400 \\ \Rightarrow 2400+25R=2575.0 \\ \Rightarrow 25R=2575-2400 \\ \Rightarrow 25R=175 \\ \Rightarrow R=\frac{175}{25} \\ \Rightarrow R=7\% \end{gathered}$$

Hence, the rate of interest $\left(R\right)$ is $7\%\mathrm{p}.\mathrm{a}.$