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A certain investment grows at an annual interest rate of 8%, [#permalink]
18 Nov 2009, 20:41

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58% (00:51) wrong based on 193 sessions

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]
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

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

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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? 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]
13 Nov 2013, 10:33

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

Re: A certain investment grows at an annual interest rate of 8%, [#permalink]
12 Aug 2014, 08:22

1

This post received KUDOS

Expert's post

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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