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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...  [#permalink]

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New post 08 Dec 2018, 08:14
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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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Re: A certain investment grows at an annual interest rate of 16 percent...  [#permalink]

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New post 08 Dec 2018, 09:34
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CAMANISHPARMAR 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) \(3 = 1.04^x\)


Standard compound interest formula => A = P *\((1+ \frac{r}{100n})^(nt)\) ; A= amount after t years ; P = principal ; r=rate of interest; n= number of times interest is compounded ; t= number of years (here t=x)
Given that A=81P ; put this in above formula.

81P = P *\((1+ \frac{16}{100*4})^(4x)\)
81 = \((1.04)^4x\) ; taking fourth root
3 = \((1.04)^x\)

E

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Re: A certain investment grows at an annual interest rate of 16 percent...  [#permalink]

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New post 07 Oct 2019, 06:32
CAMANISHPARMAR 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) \(3 = 1.04^x\)


\(A=P(1+i)^{x}…A=P(1+i/n)^{xn}…81=(1+0.16/4)^{4x}…3^4=(1.04)^{4x}…3=(1.04)^x\)

Answer (E)
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Re: A certain investment grows at an annual interest rate of 16 percent...   [#permalink] 07 Oct 2019, 06:32
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