Question : A sum of money at compound interest amounts to three times it self in three years. In how many years will it be nine times itself?
Option 1: 9 years
Option 2: 27 years
Option 3: 6 years
Option 4: 3 years
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Correct Answer: 6 years
Solution : "When compounded annually, $ A= P(1+\frac{R}{100})^{T}$, Where A is the total amount, P is the principal amount, R is the rate of interest per annum, and T is the time in years." $ A= P(1+\frac{R}{100})^{T}$ ⇒ $3P= P(1+\frac{R}{100})^{3}$ ⇒ $(1+\frac{R}{100})=3^\frac{1}{3}$............... equation1 Let after $x$ years the amount becomes 9 times. $ 9P= P(1+\frac{R}{100})^{x}$............... equation2 From equations, ⇒ $9 = 3^\frac{x}{3}$ ⇒ $3^2 = 3^\frac{x}{3}$ ⇒ $\frac {x}{3} = 2$ ⇒ $x=6$ years Hence, the correct answer is 6 years.
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