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guest612
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Post subject: fdp word bank #3 compound interest  Posted: Wed Feb 13, 2008 5:58 pm |
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Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
1-if using the formula as stated in answer, i get a different result from the latter approach using A=P(1+r/n)^nt
which is 100=P(1.04)^1. is the math incorrect?
2-the second approach is very intuitive and simple. how then would this be solved for a simple interest problem (versus it being compounded quarterly as in this problem)?
thank you!
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tkkishore
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Post subject: C.I Posted: Wed Feb 20, 2008 5:03 pm |
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100 = P (1 + 2/100)^ 2
2/100 because we are given 8% Annual rate and since compounding quarterly, you get 2% quarterly rate.
Since problem is seeking 100$ compound interest in 6 months, which is 2 quarters, you raise (1 + RT/100) portion by power of 2.
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brian
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Post subject: Posted: Thu Feb 21, 2008 1:26 am |
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| ManhattanGMAT Staff |
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Posts: 27
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Thanks tkkishore!
-Brian Lange
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guest612
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Post subject: REPLY Posted: Thu Feb 21, 2008 3:49 pm |
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Thanks! I appreciate it.
unfortunately i must be doing something blatantly wrong but doing it this way doesn't seem to yield the same result of 2500 which is the answer.
100=P(1+2/100)^2. For some reason I can't use that to get to 2500. Can you please tell me what I'm doing wrong?
Thank you very much.
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StaceyKoprince
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Post subject: Posted: Thu Feb 21, 2008 10:59 pm |
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Location: San Francisco
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Almost but not quite. The number on the left-hand side of the equation should be the principal PLUS the interest:
P+100 = P(1+ 2/100)^2
So both of the above suggested equations aren't right. Try again with the above.
In addition, the first offered equation:
100=P(1.04)^1
is also incorrect because it imposes a flat 4% rate not compounded at all (compounding something once is the same thing as saying it isn't compounded).
If you're given an annual interest rate and told to compound for some shorter amount of time, keep it in terms of the year. In this case, divide by 4 to get the 2% interest rate per quarter, and then compound it twice to get the interest after six months.
p.s. please make sure to post in correct folder - MGMAT Math Guides in this case :)
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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guest612
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Post subject: thanks! Posted: Sat Feb 23, 2008 8:04 pm |
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stacey, thanks very much for clarifying that!
i'll note the postings more carefully!
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rfernandez
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Post subject: Posted: Fri May 02, 2008 2:15 pm |
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You're welcome and thanks.
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elevinty
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Post subject: Re: fdp word bank #3 compound interest Posted: Thu Mar 17, 2011 12:20 pm |
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there is something here that is confusing me..
.the questions asks the minimum amount that will give us an interest ABOVE 100$. According to the OA 2500 will give us exactly 100$ interest; Therefore, shouldn't we choose 3000$ as a principal to get an interest OVER 100$
????
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jnelson0612
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Post subject: Re: fdp word bank #3 compound interest Posted: Sun Mar 20, 2011 3:23 pm |
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elevinty wrote: there is something here that is confusing me..
.the questions asks the minimum amount that will give us an interest ABOVE 100$. According to the OA 2500 will give us exactly 100$ interest; Therefore, shouldn't we choose 3000$ as a principal to get an interest OVER 100$
???? Please check out Stacey's explanation. Because we are compounding quarterly we will get a tiny bit more interest than if we were doing simple compounding once a year.
_________________
Jamie Nelson
ManhattanGMAT Instructor
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pratik.munjal
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Post subject: Re: fdp word bank #3 compound interest Posted: Mon Oct 24, 2011 3:07 am |
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I am still not sure why the equation has been raised to the power of 2. Perhaps you can explain that using different scenarios-in this case the time frame was 6 months, what is to be done if it is 12 months, 18 months, 24 months etc?
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StaceyKoprince
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Post subject: Re: fdp word bank #3 compound interest Posted: Sun Nov 13, 2011 11:01 pm |
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Posts: 6064
Location: San Francisco
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the exponent represents the number of periods over which the compounding happens. In this problem, we're told that the interest compounds quarterly, which means every 3 months (3 months = 1 quarter of a year). The problem also asks about a period of 6 months, so that's 2 periods of 3 months each. If the problem had asked about 12 months, we'd have used an exponent of 4, because there would be 4 periods of 3 months each, and so on.
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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