Question : A sum becomes 1.96 times itself in 2 years when invested at compound interest (compounding annually). What is the annual rate of interest?
Option 1: 20 percent
Option 2: 25 percent
Option 3: 40 percent
Option 4: 30 percent
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Correct Answer: 40 percent
Solution :
Given that, a sum becomes 1.96 times itself in 2 years.
Let the principal be $P$.
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒1.96P = P \left(1 + \frac{r}{100}\right)^2$
$⇒1.96 = \left(1 + \frac{r}{100}\right)^2$
$⇒\sqrt{1.96} = 1 + \frac{r}{100}$
$⇒\frac{r}{100} = 1.4 - 1$
$⇒r = 100 \times 0.4$
$⇒r=40\%$
Hence, the correct answer is 40 percent.
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