Question : A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years will the same amount become Rs. 8000?
Option 1: 2 years
Option 2: 4 years
Option 3: 6 years
Option 4: 8 years
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Correct Answer: 4 years
Solution :
Given:
Principal = Rs. 2000 and time = 2 years
Formula:
Amount under compound interest = $P(1+\frac{R}{100})^{n}$
Solution:
Let the rate of interest = R%
$2000(1+\frac{R}{100})^{2} = 4000$
⇒ $(1+\frac{R}{100})^{2} = \frac{4000}{2000} = 2$
⇒ $(1+\frac{R}{100}) = \sqrt{2}$ ......(i)
Let the sum amounted to Rs. 8000 in t years
⇒ $2000(1+\frac{R}{100})^{t} = 8000$
Substituting value from equation (i)
⇒ $(1+\frac{R}{100})^{t} = \frac{8000}{2000} = 4$
⇒ $(\sqrt{2})^{t} = 4$
⇒ $(2)^{\frac{t}{2}} = 2^{2}$
⇒ $\frac{t}{2} = 2$
⇒ $t = 4$ years
Hence, the correct answer is 4 years.
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