# Ex.8.3 Q7 Comparing Quantities Solutions - NCERT Maths Class 8

## Question

Maria invested Rs \(8,000 \) in a business. She would be paid interest at \(5\%\) per annum compounded annually. Find:

(i) The amount credited against her name at the end of the second year

(ii) The interest for the \(3\)^{rd }year.

## Text Solution

**What is known?**

Principal, Time Period and Rate of Interest

**What is unknown?**

Amount and Compound Interest (C.I.)

**Reasoning:**

\({A = P}\left( {{1 + }\frac{{r}}{{{100}}}} \right)^{\rm{n}}\)

\(P=\rm{Rs}\, 8,000\)

\(N =2\) years and \(3\)^{rd} year

\(R= 5\% \) p.a. compounded annually

**Steps:**

(i) For calculation of amount credited at the end of second year:

\[\begin{align}A &= P\left( {{1 + }\frac{{r}}{{{100}}}} \right)^{n} \\ &= 8000\left( {{1 + }\frac{{5}}{{{100}}}} \right)^{2} \\ &= 8000\left( {{1 + }\frac{{1}}{{{20}}}} \right)^{2} \\ &= 8000\left( {\frac{{21}}{{20}}} \right)^2 \\ & = 8000 \times \frac{{21}}{{20}} \times \frac{{21}}{{20}} \\ & = 8000 \times \frac{{441}}{{400}} \\

&= 20 \times 441 \\ & = 8820 \\

\end{align}\]

(ii) For calculating C.I. for the \(3\)^{rd} year, the principal \(= 8820\)

\[\begin{align}{\rm{S}}{\rm{.I}}{\rm{.}} &= \frac{P \times R \times T}{100}\\ &= \left( {\frac{{8820 \times 5 \times 1}}{{100}}} \right)\\&= 441\end{align}\]

The amount credited at the end of the \(2\)^{nd} year \(= \rm{Rs}\, 8,820\)

The interest for the \(3^\rm{rd} \) year \(= \rm{Rs}\, 441\)