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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