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: $3\frac{1}{2}$
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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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