A sum of money lent at compound interest for | vedclass

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Question

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=\fr

Vedclass · Accepted Answer

$40000$

Vedclass · Answer

Let the principal be Rs. P If CI is compounded half-yearly, $\Rightarrow \quad C I=P\left[\left(1+\frac{10}{100}ight)^{4}-1ight]$

(where $R=\frac{R}{2}$ s p.a. and $T=2 T$ years)

$\Rightarrow \quad C I=P\left[\left(\frac{11}{10}ight)^{4}-1ight]=\frac{4641 P}{10000}$

If CI is compounded annually, $\Rightarrow \quad C I=P\left[\left(1+\frac{20}{100}ight)^{2}-1ight]=\frac{11 P}{25}$

According to question:

$\Rightarrow \frac{4641 P }{10000}-\frac{11}{25} P =964$

$\Rightarrow P=\frac{964 	imes 10000}{241}= Rs .40000$

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 $Rs.$) ?

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