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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)

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

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

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

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com

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?

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?

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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23 May 2016, 05:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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!

gmatclubot

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

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