A certain investment grows at an annual interest rate of 16 percent

Question

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

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Nidzo · Answer

Compound Interest Formula:  A = P(1 + \frac{r}{n})^{nt}

81 = (1+ \frac{0.16}{4})^{4x}

81 = (1.04)^{4x}

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

3 = (1.04)^x

Answer E

Abhishek009 · Answer

1.04^{4x} = 3^4

So,  1.04^{x} = 3 , Answer will be (E)

KarishmaB · Answer

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* ^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/

IcanDoIt23 · Answer

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?

Bunuel · Answer

"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.

Saaaaaaaaaaaaaaa · Answer

what does it mean by " By a factor of 81". Can we consider 3 as a factor of 81 then we can write 1.04^4x = 3 which is the solution.

Bunuel · Answer

Please read the whole thread. Hope it helps.

bumpbot · Answer

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A certain investment grows at an annual interest rate of 16 percent

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A certain investment grows at an annual interest rate of 16 percent

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