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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