Question : The sum of money which when given on compound interest at 18% per annum would fetch Rs. 960 more when the interest is payable half yearly than when it was payable annually for 2 years is:
Option 1: Rs. 60,000
Option 2: Rs. 30,000
Option 3: Rs. 40,000
Option 4: Rs. 50,000
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Correct Answer: Rs. 50,000
Solution :
Given: Rate of interest = 18% and Time = 2 year
Also, Amount after Compound Interest calculated half-yearly – Amount after Compound Interest calculated yearly = Rs. 960
Now, when the interest is payable half-yearly,
Rate of interest = 9% and Time period = 4
Let the principal amount be Rs. $x$.
Compound Interest = $P((1+\frac{R}{100})^T-1)$
Then, compound interest calculated half-yearly = $x((1+\frac{9}{100})^4-1)$
= $x((\frac{109}{100})^4-1)$
= $x(1.4116-1)$
= Rs. $0.4116x$
Also, compound interest calculated yearly = $x((1+\frac{18}{100})^2-1)$
= $x((\frac{118}{100})^2-1)$
= $x(1.3924-1)$
= Rs. $0.3924x$
Now, $0.4116x-0.3924x=960$
$x=\frac{960}{0.0192}$
$x=50000$
Hence, the correct answer is Rs. 50,000.
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