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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%, 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)
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Originally posted by kairoshan on 18 Nov 2009, 21:41.
Last edited by Bunuel on 04 Feb 2014, 05:30, edited 1 time in total.
Edited the question.




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Re: compound interest
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06 Sep 2011, 20:01
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: A certain investment grows at an annual interest rate of 8%,
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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%,
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19 Nov 2009, 06:51
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
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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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Re: compound interest
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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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Re: compound interest
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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%,
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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%,
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12 Aug 2014, 09:22



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Re: A certain investment grows at an annual interest rate of 8%,
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19 Oct 2014, 06:19
81= (1.04)^4x 3^4= [(1.04)^x]^4 3=(1.04)^x.
Answer..



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Re: A certain investment grows at an annual interest rate of 8%,
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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 = 2^41.02^x = 2Could you please elaborate on the yellow part? Thanks!



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Re: A certain investment grows at an annual interest rate of 8%,
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19 Sep 2018, 18:11
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?
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) The compound interest formula is: A = P(1 + r/n)^(nt) where t = the number of years, A = the amount after t years, P = the principal or the initial amount, r = the annual interest rate, and n = the number of times compounded per year. Here, r = 8% = 0.08, n = 4, t = x. We are not given a value of P but we are given that A = 16P. So we have: 16P = P(1 + 0.08/4)^(4x) 16 = (1 + 0.02)^(4x) 16 = 1.02^(4x) Taking the fourth root of both sides of the equation, we have: 16^(¼) = [1.02^(4x)]^(¼) 2 = 1.02^x Answer: B
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Re: A certain investment grows at an annual interest rate of 8%,
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09 Oct 2018, 07:30
Bunuel wrote: 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.I have a question about ]"Increasing something by a factor of x means multiplying by x" why it is not x+x*16? there is a similar expression on OG2019"From 2000 to 2003,the number of employees at a certain company increased by a factor of 1/4 . From 2003 to 2006,the number of employees at this company decreased by a factor of 1/3. If there were 100 employees at the company in 2006, how many employees were there at the company in 2000?" here x (1+1/4)(11/3)=100; x=120




Re: A certain investment grows at an annual interest rate of 8%, &nbs
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