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

## 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 $$= \rm{Rs}\, 4,913$$

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