Question : The compound interest on Rs. 30000 at 7% per annum for $n$ years is Rs. 4347. The value of $n$ is:
Option 1: $3$ years
Option 2: $2$ years
Option 3: $4$ years
Option 4: $5$ years
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Correct Answer: $2$ years
Solution : Given: Principal, $P$ = Rs. 30000 Rate, $R$ = 7% per annum Let time be $n$ years. Compound interest, CI = Rs. 4347 Formula: Amount = $P(1+\frac{R}{100})^{n}$ Solution: Amount = $P + C.I = 30000 + 3437 = 34347$ $34347 = 30000(1+\frac{7}{100})^{n}$ $(\frac{107}{100})^{n}=\frac{34347}{30000}=\frac{11449}{10000}$ ⇒ $(\frac{107}{100})^{n}= (\frac{107}{100})^{2}$ ⇒ $n = 2$ years Hence, the correct answer is 2 years.
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