Question

If the simple interest on a sum of money for$2$years at $5\%$ per annum is Rs. $50$, what will be the compound interest on the same sum at the same rate for the same time.

Answer 1

Step 1: Find the principal or sum of money

Given- Simple Interest $(S.I.)=Rs50$

Rate of interest $(R.O.I)=$ $5\%$

$Time\left(t\right)=$ $2\mathrm{years}$

We know that simple interest $\left(S.I\right)$ for sum of money $P$ at $R\%$ rate for time $t$ is given by

$\mathrm{S}.\mathrm{I}.=\frac{\mathrm{P}\times \mathrm{T}\times \mathrm{R}}{100}$

By substituting values in the given formula

$$\begin{gathered} \Rightarrow 50=\frac{\mathrm{P}\times 2\times 5}{100} \\ \Rightarrow 50=\frac{\mathrm{P}\times 10}{100} \\ \Rightarrow 50=\frac{\mathrm{P}}{10} \\ \Rightarrow \mathrm{P}=Rs500 \end{gathered}$$

Step 2: Find the amount in compound interest

We know that Amount $\left(A\right)$ for sum of money $P$ at $R\%$ rate for time $t$ is given by in compound interest is given by

$\mathrm{A}=\left[\mathrm{P}\times {\left(1+\frac{\mathrm{R}}{100}\right)}^2\right]$

Principal $\left(P\right)=Rs500$

Rate of interest $(R.O.I)=$ $5\%$

Time$\left(t\right)=$ $2\mathrm{years}$

By substituting values in the given formula

$$\begin{gathered} \Rightarrow \mathrm{A}=\left[500\times {\left(1+\frac{5}{100}\right)}^2\right] \\ \Rightarrow \mathrm{A}=\left[500\times {\left(\frac{100+5}{100}\right)}^2\right] \\ \Rightarrow \mathrm{A}=\left[500\times \left(\frac{105}{100}\right)\times \left(\frac{105}{100}\right)\right] \\ \Rightarrow \mathrm{A}=\left[\frac{5\times 105\times 105}{100}\right] \\ \Rightarrow \mathrm{A}=551.25Rs. \end{gathered}$$

Step 3: Compound Interest

Let Compound interest $=C.I$

We know that $C.I.=A-P$

$$\begin{gathered} \Rightarrow \mathrm{C}.\mathrm{I}.=551.25-500 \\ \Rightarrow \mathrm{C}.\mathrm{I}.=51.25Rs. \end{gathered}$$

Hence, Compound interest will be 51.25 Rs.