Question

In what time $\text{Rs.}7500$ amount to $\text{Rs.}8625$.

If interest reckoned is $7\frac{1}{2}\%$ per annum.

Answer 1

Find the required value of time.

In the question, it is given that the rate of interest is $7\frac{1}{2}\%$ per annum and the principal amount is $\text{Rs.}7500$ and the final amount is $\text{Rs.}8625$.

Using the Simple Interest Formula $\mathrm{Simple}\mathrm{Interest}=\frac{\mathrm{Principle}\mathrm{Amount}\times \mathrm{Rate}\times \mathrm{Time}}{100}$.

$$\begin{gathered} \text{Rate}=\frac{\left(7\times 2\right)+1}{2}\% \\ \Rightarrow \text{Rate}=\frac{15}{2}\% \end{gathered}$$

So, the rate of interest is $\frac{15}{2}\%$ per annum.

And, $\text{Simple Interest = Final Amount- Principal Amount}$

$$\begin{gathered} \text{Simple Interest=}8625-7500 \\ \Rightarrow \text{Simple Interest=1125} \end{gathered}$$

Let, time be $\mathrm{t}$ years and then apply the Simple Interest Formula.

$$\begin{gathered} 1125=\frac{7500\times 15\times \mathrm{t}}{100\times 2} \\ \Rightarrow \mathrm{t}=\frac{2250}{1125} \\ \Rightarrow \mathrm{t}=2\mathrm{years} \end{gathered}$$

Hence in $2$Years $Rs.7500$ amount to $Rs.8625$ at rate $7.5\%$ per annum.