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
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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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