Question : If a sum is invested at simple interest, then it becomes $\frac{3}{2}$ of itself in 4 years. What is the annual rate of interest?
Option 1: 6.5 percent
Option 2: 12.5 percent
Option 3: 17.5 percent
Option 4: 10 percent
Correct Answer: 12.5 percent
Solution :
The sum becomes $\frac{3}{2}$ times itself in 4 years
⇒ $P +\frac{P×R×T}{100} = \frac{3}{2}$$P$
⇒ $P+\frac{P×R×4}{100} = \frac{3}{2}$$P$
⇒ $1+\frac{R×4}{100} = \frac{3}{2}$
⇒ $\frac{R×4}{100} = \frac{1}{2}$
⇒ R = $\frac{1}{2} × \frac{100}{4}$
⇒ R = $\frac{25}{2}$ = 12.5%
Hence, the correct answer is 12.5 percent.
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