# Ex.8.3 Q5 Comparing Quantities Solution - NCERT Maths Class 8

## Question

Vasudevan invested $$\rm{Rs}\, 60,000$$ at an interest rate of $$12\%$$ per annum compounded half yearly. What amount would he get

(i) after $$6$$ months?

(ii) after $$1$$ year?

Video Solution
Comparing Quantities
Ex 8.3 | Question 5

## Text Solution

What is known?

Principal, Time Period and Rate of Interest

What is unknown?

Amount and Compound Interest (C.I.)

Reasoning:

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

$$P =\rm{ Rs}\,60,000$$

$$N =6$$ months and $$1$$ year

$$R =12\%$$ p.a. compounded half yearly

Steps:

For easy calculation of compound interest, we will put Interest Rate as $$6\%$$ half yearly and $$'n'$$ as $$1$$

(i) Compound Interest to be paid for $$6$$ month

\begin{align}A & = P{\left( {{1 + }\frac{{r}}{{{100}}}} \right)^{n}}\\& = 60000{\left( {{1 + }\frac{{6}}{{{100}}}} \right)^{1}}\\& = 60000{\left( {\frac{{100}}{{100}} + \frac{{6}}{{{100}}}} \right)^{1}}\\& = 60000\left( {\frac{{{106}}}{{{100}}}} \right)\\&= {60000} \times {1}{.06}\\&= 63600\end{align}

Compound Interest for $$6$$ month

\begin{align} &= 63600 - 60000\\&= 3600\end{align}

(ii) Compound Interest to be paid for $$12$$ months ($$1$$ year) Compounded half yearly So $$n=2,r=6\%,$$

\begin{align}A &= P{\left( {{1 + }\frac{{r}}{{{100}}}} \right)^{n}}\\&= 60000{\left( {{1 + }\frac{{6}}{{{100}}}} \right)^{2}}\\& = 60000{\left( {\frac{{100}}{{100}} + \frac{{6}}{{{100}}}} \right)^{2}}\\& = 60000{\left( {\frac{{{106}}}{{{100}}}} \right)^2}\\& = 60000\left( {\frac{{{106} \times {106}}}{{{100} \times 100}}} \right)\\& = 60000\left( {\frac{{11236}}{{{100}00}}} \right)\\&= {60000} \times {1}{.1236}\\&= 67416\end{align}

Compound Interest for $$12$$ months

\begin{align} &= 67416 - 60000\\&= 7416\end{align}

The amount that Vasudevan will get after $$6$$ months $$= \rm{Rs}\,63600$$

The amount that Vasudevan will get after $$1$$ year  $$= \rm{Rs}\, 67416$$

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