Question : In how many years will Rs. 40000 amounts to Rs. 46656 at the rate of 8% compound interest per annum.
Option 1: 5
Option 2: 2
Option 3: 4
Option 4: 3
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Correct Answer: 2
Solution :
Given that Total amount = Rs. 46656, Principal = Rs. 40000, and Rate = 8%
Let time be $n$ years.
We know that, $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$⇒46656 = 40000 \left(1 + \frac{8}{100}\right)^n$
$ ⇒\frac{46656}{40000}=\left(1 + \frac{8}{100}\right)^n$
$ ⇒\frac{11664}{10000}=\left( \frac{108}{100}\right)^n$
$⇒ (\frac{108}{100})^2=\left( \frac{108}{100}\right)^n$
$\therefore n=2$
Hence, the correct answer is 2.
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