Question : At what time will Rs. 1000 become Rs. 1331 at 10% per annum compounded annually?
Option 1: 3
Option 2: $2\frac{1}{2}$
Option 3: 2
Option 4: $3\frac{1}{2}$
Correct Answer: 3
Solution :
Let the time be $n$.
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒1331=1000(1+\frac{10}{100})^n$
$⇒1331=1000(\frac{110}{100})^n$
$⇒ \frac{1331}{1000}=(\frac{11}{10})^n$
$⇒ (\frac{11}{10})^3=(\frac{11}{10})^n$
After comparing, we get:
$n=3$
Hence, the correct answer is 3.
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