Question : Rekha invested a sum of Rs. 12000 at 5% per annum compound interest. She received an amount of Rs. 13230 after $n$ years. Find $n$.
Option 1: 2.8 years
Option 2: 3 years
Option 3: 2.5 years
Option 4: 2 years
Correct Answer: 2 years
Solution :
Total amount = Rs. 13230
Sum = Rs. 12000
Rate = 5%
Let $n$ be the time.
We know, $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒13230 = 12000(1+\frac{5}{100})^{n}$
$⇒\frac{13230}{12000} =(\frac{21}{20})^{n}$
$⇒\frac{441}{400} =(\frac{21}{20})^{n}$
$⇒(\frac{21}{20})^2 =(\frac{21}{20})^{n}$
$\therefore n= 2$
Hence, the correct answer is 2 years.
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