If a sum of money at compound interest amount to thrice itself in 3 years then in how many years wil...........

Quantitative Aptitude ( CCS) Compound Interest

If a sum of money at compound interest amount to thrice itself in 3 years, then in how many years will it be 9 times itself?

9 years

6 years

7 years

None of these

Using the conditions given the amount after 3 years is thrice the principal : A=3P

So A =P(1 + r/100)^n

3P = P(1+ r/100)^3

(1+r/100) =3^1/3

Now for the second case let A = 9P in n years

Therefore, 9P = P(1+r/100)^n

9 = (1+r/100)^n

From above putting the value of (1+r/100)=3^1/3

9=(3^1/3)^n

3^2=3^n/3 using indices

So 2= n/3 equating the indices

n= 6

Hence, option 2 is the correct answer.

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