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Ruben
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Post subject: MAGMAT - A certain investment grows  Posted: Sun Jun 08, 2008 10:45 pm |
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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
I can't understand what the question is really asking. The explanations says:
At the end of the x years, the final value, F, will be equal to 16 times the principal (the money is growing by a factor of 16).
Therefore, F = 16P.
r = .08 (8% annual interest rate)
n = 4 (compounded quarterly)
t = x (the question is asking us to express the time in terms of x number of years)
We can write the equation
16P = P (1 + .08/4)4x
16 = (1.02)4x
Could you please help me rephrasing the question? Is it asking to find a formula that allows us to obtain a a value of 16 after x years of compunding interest?
Thanks,
Ruben
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RonPurewal
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Post subject: Re: MAGMAT - A certain investment grows Posted: Thu Jun 12, 2008 6:26 am |
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| ManhattanGMAT Staff |
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Posts: 7146
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Ruben wrote: Could you please help me rephrasing the question? Is it asking to find a formula that allows us to obtain a a value of 16 after x years of compunding interest?
not really, although the '16' is what you end up with after the appropriate cancellations.
make sure you know how to use the compound interest formula, P*(1 + r/n)^(nt), where P is the principal at the beginning, r is the interest rate PER YEAR (as a decimal, e.g., 0.07 for 7%), n is the number of compounding periods per year (e.g., n = 4 for quarterly compounding), and t is time IN YEARS.
that's what gives the formula in this problem.
note that the 16 is originally 16P: you start with principal 'P', and you want to find the time that the investment takes to reach '16P'. you can then cancel the 'P's that appear on both sides. (alternatively, since the phrasing of the problem makes it clear that the original principal is irrelevant - because it's never mentioned - you can just pick a number for P.)
make sense?
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Ruben
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Post subject: Posted: Sun Jun 15, 2008 2:57 pm |
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Ron,
I think I got it. I was thrown off by the wording a factor of 16. When y increasey by a factor of x means I multiply y by x right?
Thanks,
Ruben
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RonPurewal
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Post subject: Posted: Sun Jun 15, 2008 11:03 pm |
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| ManhattanGMAT Staff |
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Posts: 7146
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Ruben wrote: When y increasey by a factor of x means I multiply y by x right?
correct.
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lanzhou1
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Post subject: Re: MAGMAT - A certain investment grows Posted: Sat Apr 17, 2010 1:44 pm |
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Posts: 2
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My solution on the CAT is 2 = (1.02)^x.
There is a paragraph in addition to the explanation copied above. After the solution calculated 16 = (1.02)^(4x) (which is what I got) it also says:
_______________________________________________
"Now we can take the fourth root of both sides of the equation. (i.e.the equivalent of taking the square root twice) We will only consider the positive root because a negative 2 doesn't make sense here.
161/4 = [(1.02)^(4x)]^(1/4)
2 = (1.02)^x
The correct answer is B."
________________________________________________
My question is... why do you take the 4th root? I'm not sure of the logic here
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lanzhou1
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Post subject: Re: MAGMAT - A certain investment grows Posted: Mon Apr 19, 2010 1:08 pm |
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Nevermind, I got it. Just needed to find an equivalent equation.
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tim
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Post subject: Re: MAGMAT - A certain investment grows Posted: Fri Apr 30, 2010 7:00 pm |
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| ManhattanGMAT Staff |
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Posts: 2242
Location: Southwest Airlines, seat 21C
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Glad to hear it!
_________________
Tim Sanders
Manhattan GMAT Instructor
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marc.gagnon
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Post subject: Re: MAGMAT - A certain investment grows Posted: Mon May 16, 2011 2:41 pm |
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Can you help clarify "increase by a factor of 16".
If I have $5 and it increases by a factor of 1, do I now I have $5 or $10 (original $5 + increase $5)?
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jnelson0612
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Post subject: Re: Posted: Sun May 22, 2011 9:39 pm |
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Posts: 1857
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Marc, check this post out: RonPurewal wrote: Ruben wrote: When y increases by a factor of x means I multiply y by x right? correct.
_________________
Jamie Nelson
ManhattanGMAT Instructor
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marc.gagnon
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Post subject: Re: MAGMAT - A certain investment grows Posted: Tue Jun 07, 2011 3:05 pm |
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Thanks
Can you help confirm/clarify my understanding for similiar phrasings:
Three times as many as X: Means X * 3
Four times greater than X: Means X * 4 + X, which simplifies to X * 5
Am I missing any other ones?
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jnelson0612
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Post subject: Re: MAGMAT - A certain investment grows Posted: Sat Jun 25, 2011 1:55 pm |
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marc.gagnon wrote: Thanks
Can you help confirm/clarify my understanding for similiar phrasings:
Three times as many as X: Means X * 3
Four times greater than X: Means X * 4 + X, which simplifies to X * 5
Am I missing any other ones? Those look correct to me. Marc has three times as many apples as I do. If you have 12 apples, I have 4. Marc earns a salary that is 4 times greater than mine. If mine is $20, and Marc's is 4 times greater than that, his must be $80 greater, or $100. I don't think you're necessarily missing anything; if you ever are in doubt, plug real numbers to help you figure these out.
_________________
Jamie Nelson
ManhattanGMAT Instructor
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