Question

Haneef has a cumulative bank account and deposits Rs. 600 per month for a period of 4 years. If he gets Rs. 5,880 as interest at the time of maturity. Find the rate of interest.

Answer 1

Step 1: Given data:

Instalments per month, $\left(P\right)=\mathrm{Rs}.600$

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

Interest received by Haneef, $\left(I\right)=\mathrm{Rs}.5880$

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 rate of interest:

Let the rate of interest be $R\%$ p.a.

Then,

$\begin{array}{rcl}\mathrm{Interest}& =& P\mathit{\times }\frac{n\left(n\mathit{+}\mathit{1}\right)}{2\times 12}\mathit{\times }\frac{R}{\mathit{100}}\\ & \Rightarrow & 5880\mathit{=}\mathit{600}\mathit{\times }\frac{\mathit{48}\left(\mathit{48}\mathit{+}\mathit{1}\right)}{\mathit{2}\mathit{\times }\mathit{12}}\mathit{\times }\frac{R}{\mathit{100}}\\ & \Rightarrow & 5880\mathit{=}\mathit{600}\mathit{\times }\frac{\mathit{48}\times 49}{\mathit{2}\mathit{\times }\mathit{12}}\mathit{\times }\frac{R}{\mathit{100}}\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{\Rightarrow }& \mathit{5880}\mathit{=}\mathit{600}\mathit{\times }\frac{\mathit{48}\mathit{\times }\mathit{49}}{\mathit{2400}}\mathit{\times }R\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{\Rightarrow }& \mathit{5880}\mathit{=}\frac{\mathit{48}\mathit{\times }\mathit{49}}{\mathit{4}}\mathit{\times }R\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{\Rightarrow }& \mathit{5880}\mathit{=}\mathit{12}\mathit{\times }\mathit{49}\mathit{\times }R\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{\Rightarrow }& \mathit{5880}\mathit{=}\mathit{588}\mathit{\times }R\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{\Rightarrow }& R\mathit{=}\frac{\mathit{5880}}{\mathit{588}}\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}& \mathit{\Rightarrow }& R\mathit{=}\mathit{10}\\ \mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{}\mathit{\therefore }R& \mathit{=}& \mathit{10}\mathit{\%}\mathit{}\mathrm{p}.\mathrm{a}.\end{array}$

Hence, the rate of interest is $10\%$ per annum.