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Re: A certain investment grows at an annual interest rate of 16 percent [#permalink]
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Bunuel wrote:
A certain investment grows at an annual interest rate of 16 percent, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81?


(A) \(81 = 1.16^{4x}\)

(B) \(81 = 1.04^x\)

(C) \(3 = 1.16^x\)

(D) \(3 = 1.04^{4x}\)

(E) \(3 = 1.04^x\)

Are You Up For the Challenge: 700 Level Questions


Compound interest is simply successive percentage increase of r%.
If annual rate is 16%, the quarterly rate will be 4% applied 4 times in a year.
If Amount has to increase by a factor of 81, it means if principal is 1, the amount becomes 81.

\(81 = 1*[(1+ 0.4)*(1+ 0.4)*(1+ 0.4)*(1+ 0.4)]^x\)

\(3^4 = 1.04^{4x}\)

Taking the fourth root, we get

3 = 1.04^x
which we need to solve to get x.

Answer (E)

Check this post for a discussion on successive percentage changes: https://anaprep.com/arithmetic-successi ... e-changes/
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Re: A certain investment grows at an annual interest rate of 16 percent [#permalink]
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Bunuel wrote:
A certain investment grows at an annual interest rate of 16 percent, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81?


(A) \(81 = 1.16^{4x}\)

(B) \(81 = 1.04^x\)

(C) \(3 = 1.16^x\)

(D) \(3 = 1.04^{4x}\)

(E) \(3 = 1.04^x\)

Are You Up For the Challenge: 700 Level Questions

­The question says that the amount is increased "by" a factor of 81 and not "to" a factor 81. Isn't the total amount should be (81+1)*(Initial Amount). 

Could you help explain with an example the mistake I'm making?
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A certain investment grows at an annual interest rate of 16 percent [#permalink]
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Expert Reply
ssinghal087 wrote:
Bunuel wrote:
A certain investment grows at an annual interest rate of 16 percent, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 81?


(A) \(81 = 1.16^{4x}\)

(B) \(81 = 1.04^x\)

(C) \(3 = 1.16^x\)

(D) \(3 = 1.04^{4x}\)

(E) \(3 = 1.04^x\)

Are You Up For the Challenge: 700 Level Questions

­The question says that the amount is increased "by" a factor of 81 and not "to" a factor 81. Isn't the total amount should be (81+1)*(Initial Amount). 

Could you help explain with an example the mistake I'm making?

­"Increasing by a factor of x" means multiplying by x. For example, if 10 is increased by a factor of 5, the result is 10*5 = 50.

"Decreasing by a factor of x" means dividing by x. For example, if 10 is decreased by a factor of 5, the result is 10/5 = 2.

Hope this helps.­
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A certain investment grows at an annual interest rate of 16 percent [#permalink]
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