Question : On a certain sum of money, the difference between the compound interest for a year, payable half-yearly and the simple interest for a year is Rs. 180. If the rate of interest in both cases is 10%, then the sum is:
Option 1: Rs. 60000
Option 2: Rs. 72000
Option 3: Rs. 62000
Option 4: Rs. 54000
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Correct Answer: Rs. 72000
Solution :
Given:
When interest is calculated half yearly interest is halved i.e. 5%.
Number of period = 2
We know,
Simple interest, SI = $\frac{\text{Principal × Rate × Time}}{100}$
Compound Interest, CI = $P(1+\frac{R}{100})^{n}-P$, where $P$ is the principal, $R$ is the rate, and $n$ is the time period.
SI = $\frac{P \times 10 \times 1}{100} = \frac{P}{10}$
CI = $P((1+\frac{5}{100})^{2}-1) = P\times \frac{41}{400}$
According to the question,
$P\times\frac{41}{400}-\frac{P}{10}= 180$
⇒ $P\times\frac{1}{400} = 180$
$\therefore P = 72000$
Hence, the correct answer is Rs. 72000.
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