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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] New post 18 Nov 2009, 20:41
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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, 04:30, 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] New post 18 Nov 2009, 22:52
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] New post 19 Nov 2009, 05:51
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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

B is the answer...

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

Thanks!
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compound interest [#permalink] New post 06 Sep 2011, 18:49
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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Re: compound interest [#permalink] New post 06 Sep 2011, 19:01
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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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Re: compound interest [#permalink] New post 06 Sep 2011, 19:10
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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Re: compound interest [#permalink] New post 07 Sep 2011, 08:18
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] New post 13 Nov 2013, 10:33
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Re: A certain investment grows at an annual interest rate of 8%, [#permalink] New post 03 Aug 2014, 04:39
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] New post 12 Aug 2014, 08:22
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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] New post 19 Oct 2014, 05:19
81= (1.04)^4x
3^4= [(1.04)^x]^4
3=(1.04)^x.

Answer..
Re: A certain investment grows at an annual interest rate of 8%,   [#permalink] 19 Oct 2014, 05:19
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