Question : The simple interest received on a sum is $\frac{4}{9}$ of the sum. The number of years is equal to the annual rate of interest. What is the annual rate of interest?
Option 1: 7.5%
Option 2: 6.66%
Option 3: 6%
Option 4: 5.25%
Correct Answer: 6.66%
Solution :
Given: Simple interest = $\frac{4}{9}$ of Principal
Let rate = time = $x$
$\frac{\text{Simple interest}}{\text{Principal}}=\frac{4}{9}$
Now, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $\frac{\text{Simple interest}}{\text{Principal}} = \frac{x × x}{100}$
⇒ $x^2=\frac{400}{9}$
⇒ $x=\frac{20}{3}=6.66$$
Hence, the correct answer is 6.66%.
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