Question

An investment earns $4\mathrm{paise}$ per rupee invested. If at the end of the year, the interest earned by investment is $₹100$, then the investment is equal to?

Answer 1

Given, the investment earns $4\mathrm{paise}$ per rupee invested.

i.e. if the principal is $₹1$, then interest is $4\mathrm{paise}=₹\frac{4}{100}$

Step 1: Calculate the rate of interest

We know that $\mathrm{Interest}=\frac{\mathrm{Principal}\times \mathrm{Rate}\mathrm{of}\mathrm{interest}\times Time}{100}$

$$\begin{gathered} \Rightarrow \frac{4}{100}=\frac{1\times \mathrm{R}\%\times 1}{100} \\ \Rightarrow 4=\mathrm{R}\% \\ \Rightarrow \mathrm{R}=4\% \end{gathered}$$ (Where $\mathrm{R}\%$ is the rate of interest.)

Step 2: Calculate the new investment

If interest is $₹100$, then investment or principal can be calculated as shown below:

$\because \mathrm{Interest}=\frac{\mathrm{Principal}\times \mathrm{Rate}\mathrm{of}\mathrm{interest}\times Time}{100}$

$\Rightarrow 100=\frac{\mathrm{x}\times 4\times 1}{100}$ (Where $\mathrm{x}$ is the new investment.)

$$\begin{gathered} \Rightarrow 4\mathrm{x}=10000 \\ \Rightarrow \mathrm{x}=\frac{10000}{4} \\ \Rightarrow \mathrm{x}=2500 \end{gathered}$$

Therefore the investment is equal to $₹2500$.