Question : A sum of money invested at 20% compound interest (compounded annually). It would fetch Rs. 723 more in 2 years if interest is compounded half-yearly. The sum is:
Option 1: Rs. 15,000
Option 2: Rs. 30,000
Option 3: Rs. 20,000
Option 4: Rs. 7,500
Correct Answer: Rs. 30,000
Solution :
We have,
$R = 20\%$, and $T = 2$.
Let the principal be Rs. $P$.
When interest is compounded annually,
$\text{Compound interest} = P[(1 + \frac{R}{100})^{t}-1]$
$CI=P[(1+\frac{20}{100})^2-1]$
$CI=P[(\frac{6}{5})^2-1]=\frac{11P}{25}$
When the interest is compounded half-yearly,
$CI=P[(1+\frac{10}{100})^4-1]$
$CI=P[(\frac{11}{10})^2-1]$
$CI=P[(\frac{14641}{10000})-1]=\frac{4641P}{10000}$
From the question,
$⇒\frac{4641P}{10000}-\frac{11P}{25}=723$
$⇒\frac{4641P-4400P}{10000}=723$
$⇒\frac{241P}{10000}=723$
$⇒P = 30000$
Hence, the correct answer is Rs. 30,000.
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