Question : If at compound interest a certain sum becomes 2 times itself in 5 years, then in how many years will it become 8 times itself?
Option 1: 18 years
Option 2: 12 years
Option 3: 20 years
Option 4: 15 years
Correct Answer: 15 years
Solution :
Given: The compound interest of a certain sum becomes 2 times itself in 5 years.
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
According to the question,
$2P=P[1+\frac{R}{100}]^5$
⇒ $2=[1+\frac{R}{100}]^5$-------------(1)
The number of years it becomes 8 times itself,
So, $8P=P[1+\frac{R}{100}]^T$
⇒ $2^3=[1+\frac{R}{100}]^T$----------------(2)
From equation (1) and equation (2), we get,
⇒ $([1+\frac{R}{100}]^5)^3=[1+\frac{R}{100}]^T$
⇒ $[1+\frac{R}{100}]^{15}=[1+\frac{R}{100}]^T$
⇒ $T=15$ years
Hence, the correct answer is 15 years.
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