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

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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 \(= \rm{Rs}\, 441\)