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Ex.8.3 Q9 Comparing Quantities Solutions - NCERT Maths Class 8

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Question

Find the amount which Ram will get on \(\rm{Rs}\; 4,096\), if he gave it for \(18\) months at \( 12\begin{align}\frac{1}{2}\% \end{align}\) per annum, interest being compounded half yearly.

 Video Solution
Comparing Quantities
Ex 8.3 | Question 9

Text Solution

What is known?

Principal, Time Period and Rate of Interest

What is unknown?

Amount

Reasoning:

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

\(P=\rm{Rs}\,4,096\)

\(N =18\) months

\(R =12\begin{align}\frac{1}{2}\% \end{align}\) p.a. compounded half-yearly

Steps:

For calculation of C.I. compounded half yearly, we will take Interest rate as \(6\begin{align}\frac{1}{4}\% \; = \;\frac{{25}}{4}\%\end{align} \) and  \('n'\) as \(3\) \((18\div 6= 3)\)

\[\begin{align}A &= P\left( {{1 + }\frac{{r}}{{{100}}}} \right)^{n}  \\ &= 4096\left( {{1 + }\frac{{{25}}}{{{100} \times {4}}}} \right)^{3}  \\ & = 4096\left( {{1 + }\frac{{{25}}}{{{400}}}} \right)^{3}  \\ 
 & = 4096\left( {\frac{{425}}{{400}}} \right)^3  \\ & = 4096\left( {\frac{{17}}{{16}}} \right)^3  \\ 
 & = 4096 \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} \times \frac{{17}}{{16}} \\ &= 4096 \times \frac{{4913}}{{4096}} \\ &= 4913 \\ \end{align}\]

The total amount that Ram will get at the end of \(18\) months \( = \rm{Rs}\, 4,913\)