Question : If the amount is $3\frac{3}{8}$ times the sum after 3 years at compound interest compounded annually, then the Rate of interest per annum is:
Option 1: $25$%
Option 2: $50$%
Option 3: $16\frac{2}{3}$%
Option 4: $33\frac{1}{3}$
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Correct Answer: $50$%
Solution :
Let the principal be Rs. $x$.
Rate of interest = R%
Time = 3 years
Amount = $3\frac{3}{8}=3.375x$
We know, $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒3.375x = x(1 + \frac{R}{100})^{3}$
$⇒3.375 =(1 + \frac{R}{100})^{3}$
$⇒(1 + \frac{R}{100})^{3} = (1.5)^{3}$
$⇒(1 + \frac{R}{100}) = (1.5)$
$⇒\frac{R}{100}=0.5$
$\therefore R=50$%
Hence, the correct answer is $50$%.
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