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 $$= \rm{Rs}\, 441$$

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