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A certain investment grows at an annual interest rate of 8%,

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A certain investment grows at an annual interest rate of 8%, [#permalink]

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18 Nov 2009, 21:41
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A certain investment grows at an annual interest rate of 8%, 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 16?

A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Feb 2014, 05:30, edited 1 time in total.
Edited the question.

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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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18 Nov 2009, 23:52
kairoshan wrote:
A certain investment grows at an annual interest rate of 8%, 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 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

B -> 2 = (1.02)^x

PS: this should be in Problem Solving forum

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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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19 Nov 2009, 06:51
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If P is the principle:

16*P = P*(1+8/400)^(4x)

which can be reduced to:2 = (1.02)^x

BUT... can we really simplify x^4=y^(4*z) to x=y^z?

Thanks!

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06 Sep 2011, 19:49
A certain investment grows at an annual interest rate of 8%, 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 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

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06 Sep 2011, 20:01
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ssruthi wrote:
A certain investment grows at an annual interest rate of 8%, 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 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

If we apply 8% annual interest, compounded quarterly, then we apply one quarter of the interest (or 2% interest) four times per year. That is, in one year, we will multiply the value of our investment by 1.02 four times, or in other words, by (1.02)^4. So, if we invest for x years, we will apply 2% interest 4x times, so will multiply the value of our initial investment by (1.02)^(4x). Now, we know that the value has increased by a factor of 16, so

(1.02)^(4x) = 16
(1.02^x)^4 = 2^4
1.02^x = 2
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06 Sep 2011, 20:10
IanStewart wrote:
ssruthi wrote:
A certain investment grows at an annual interest rate of 8%, 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 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

If we apply 8% annual interest, compounded quarterly, then we apply one quarter of the interest (or 2% interest) four times per year. That is, in one year, we will multiply the value of our investment by 1.02 four times, or in other words, by (1.02)^4. So, if we invest for x years, we will apply 2% interest 4x times, so will multiply the value of our initial investment by (1.02)^(4x). Now, we know that the value has increased by a factor of 16, so

(1.02)^(4x) = 16
(1.02^x)^4 = 2^4
1.02^x = 2

Thanks, i was confused with 8% annual rate.
If the question was like 8% interest rate means we will take 1.08 only rgt?

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07 Sep 2011, 09:18
yup.. but usually gmac specifies whether the rate is annual or compunded quarterly.. so hopefully we should not ee any ambiguous content

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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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13 Nov 2013, 11:33
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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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03 Aug 2014, 05:39
A certain investment grows at an annual interest rate of 8%, 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 16?[/b]

I am confused by the wording here:

It is implied in the OA that "increase by a factor of 16" means that the Amount increased to 16 times its original amount.

Don't you think that "increase by a factor of 16" means [b]x + 16x?

Hope an expert clarifies this doubt!

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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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12 Aug 2014, 09:22
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pratikshr wrote:
A certain investment grows at an annual interest rate of 8%, 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 16?[/b]

I am confused by the wording here:

It is implied in the OA that "increase by a factor of 16" means that the Amount increased to 16 times its original amount.

Don't you think that "increase by a factor of 16" means [b]x + 16x?

Hope an expert clarifies this doubt!

Increasing something by a factor of x means multiplying by x.
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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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19 Oct 2014, 06:19
81= (1.04)^4x
3^4= [(1.04)^x]^4
3=(1.04)^x.

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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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23 May 2016, 05:59
Hello from the GMAT Club BumpBot!

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Re: A certain investment grows at an annual interest rate of 8%, [#permalink]

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02 Sep 2016, 14:41
IanStewart wrote:
ssruthi wrote:
A certain investment grows at an annual interest rate of 8%, 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 16?
16 = (1.02)x/4
2 = (1.02)x
16 = (1.08)4x
2 = (1.02)x/4
1/16 = (1.02)4x

If we apply 8% annual interest, compounded quarterly, then we apply one quarter of the interest (or 2% interest) four times per year. That is, in one year, we will multiply the value of our investment by 1.02 four times, or in other words, by (1.02)^4. So, if we invest for x years, we will apply 2% interest 4x times, so will multiply the value of our initial investment by (1.02)^(4x). Now, we know that the value has increased by a factor of 16, so

(1.02)^(4x) = 16
(1.02^x)^4 = 2^4
1.02^x = 2

Could you please elaborate on the yellow part?

Thanks!

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Re: A certain investment grows at an annual interest rate of 8%,   [#permalink] 02 Sep 2016, 14:41
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