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

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Director
Joined: 12 Feb 2015
Posts: 961
A certain investment grows at an annual interest rate of 16 percent...  [#permalink]

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08 Dec 2018, 08:14
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Difficulty:

95% (hard)

Question Stats:

33% (01:51) correct 67% (01:42) wrong based on 92 sessions

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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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Manish

"Only I can change my life. No one can do it for me"
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Joined: 24 Jun 2013
Posts: 141
Location: India
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Re: A certain investment grows at an annual interest rate of 16 percent...  [#permalink]

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08 Dec 2018, 09:34
1
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

pls bear with the formatting
Director
Joined: 24 Nov 2016
Posts: 935
Location: United States
Re: A certain investment grows at an annual interest rate of 16 percent...  [#permalink]

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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) $$3 = 1.04^x$$

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

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