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- Quantitative Aptitude
A sum of money lent at compound interest for $2 \,yr$ at $20 \%$ pa would fetch $Rs. 964$ more, if the interest was payable half-yearly than if it was payable annually. What is the sum (In $Rs.$) ?
$40000$
$60000$
$90000$
$500000$
Solution
Let the principal be Rs. P If CI is compounded half-yearly, $\Rightarrow \quad C I=P\left[\left(1+\frac{10}{100}\right)^{4}-1\right]$
(where $R=\frac{R}{2}$ s p.a. and $T=2 T$ years)
$\Rightarrow \quad C I=P\left[\left(\frac{11}{10}\right)^{4}-1\right]=\frac{4641 P}{10000}$
If CI is compounded annually, $\Rightarrow \quad C I=P\left[\left(1+\frac{20}{100}\right)^{2}-1\right]=\frac{11 P}{25}$
According to question:
$\Rightarrow \frac{4641 P }{10000}-\frac{11}{25} P =964$
$\Rightarrow P=\frac{964 \times 10000}{241}= Rs .40000$
