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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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The answer is D.

Gmatnub - you forgot to raise it to the n number of years. (disregard this)

Guess it's C.

I was thinking simple is compounded annually rather than monthly, but it's not compounded at all.

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It take a big man to admit when he's wrong. It takes an even bigger man to laugh at that man for being wrong.


gmat blows wrote:
I know this problem may seem easy to the business savy people...but as an engineer, I dont know any of these formulas...

If $10,000 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?
A) 10,000(x^n)
B) 10,000(x/100)^n
C) 10,000n(x/100)
D) 10,000(1+x/100)^n
E) 10,000n(1+x/100)

----
This is a GMATPrep question and I'm surprised that GMAT would just ask such a direct question as asking to regurgitate a formula - is there a trick to this that I did not pick up on?? BTW, I picked D (I swear, I've seen that formula floating around...but apparently I'm wrong)

thanks.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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thanks, OA is C.

missed the point that it was only asking for interest, not the TOTAL (principal + interest)
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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I used the plug in method.

If X = 10 and n = 2, after one year 1,000 dollars in interest will be earned (11,000 total). After the second year, 1,100 dollars in interest will be earned (12,100 total in account). Interest earned = 12,100 - 10,000 = 2,100.

A quick scan of the answer choices (plugging in X= 10 and n = 2) tells you that only C is close to 2100, and is the answer.

But C = 10000 (2) (.1) = 2000. This is Slightly less than the 2100 I got above.

I wonder if the plug in method is an estimation, or if I screwed up the math somewhere. In any event, the plug in method is good when you have no idea what formula is correct or when you have no idea how to solve the algebra.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
I encountered this problem recently on a GMATPrep test. I used the plugging in method and went wrong.

I made a silly mistake which I realized while looking at the OA but did not realize it when actually solving the problem.

Let the rate of interest = 10% hence I plugged in x as (10/100) in the answer choices and hence ended up with choice A which was wrong.

I should have taken x as it is i.e. x=10 instead of x/100. The x percent took me for a ride here. :)

Overall, thinking back, this was a straightforward Simple Interest formula problem i.e.

Simple Interest = (Principal*Number Of Years*Rate of interest)/100 i.e. (PNR)/100
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
dear all,

so if the formula for simple interest rate is I = P * R * T
then what is the name / kind of interest rate with formula F = P ( 1+R/100 )^T ??

now am confused in which problem i should use either formula.

thanks in advance!
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
sayno wrote:
dear all,

so if the formula for simple interest rate is I = P * R * T
then what is the name / kind of interest rate with formula F = P ( 1+R/100 )^T ??

now am confused in which problem i should use either formula.

thanks in advance!



That's the compound interest formula
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
tamg08 wrote:
I used the plug in method.

If X = 10 and n = 2, after one year 1,000 dollars in interest will be earned (11,000 total). After the second year, 1,100 dollars in interest will be earned (12,100 total in account). Interest earned = 12,100 - 10,000 = 2,100.

A quick scan of the answer choices (plugging in X= 10 and n = 2) tells you that only C is close to 2100, and is the answer.

But C = 10000 (2) (.1) = 2000. This is Slightly less than the 2100 I got above.

I wonder if the plug in method is an estimation, or if I screwed up the math somewhere. In any event, the plug in method is good when you have no idea what formula is correct or when you have no idea how to solve the algebra.



Tried this too but just like you said it comes down to 2000 and not 2100. Almost seems like the formula doesnt work to me?
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
JoostGrijsen wrote:
tamg08 wrote:
I used the plug in method.

If X = 10 and n = 2, after one year 1,000 dollars in interest will be earned (11,000 total). After the second year, 1,100 dollars in interest will be earned (12,100 total in account). Interest earned = 12,100 - 10,000 = 2,100.

A quick scan of the answer choices (plugging in X= 10 and n = 2) tells you that only C is close to 2100, and is the answer.

But C = 10000 (2) (.1) = 2000. This is Slightly less than the 2100 I got above.

I wonder if the plug in method is an estimation, or if I screwed up the math somewhere. In any event, the plug in method is good when you have no idea what formula is correct or when you have no idea how to solve the algebra.



Tried this too but just like you said it comes down to 2000 and not 2100. Almost seems like the formula doesnt work to me?



Same here.
Luckily, I had first pluged-in x=10, n=1. Thus, narrowing the possibilities to B(=1000) and C(=1000).
Using n=2 on B and C alone, made C to appear stronger, even if it havn't given me the correct answer.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
sayno wrote:
dear all,

so if the formula for simple interest rate is I = P * R * T
then what is the name / kind of interest rate with formula F = P ( 1+R/100 )^T ??

now am confused in which problem i should use either formula.

thanks in advance!




Compound interest formula is-

Principal * (1+ ( Rate/C) * Time^C

C= Number of times the principal is compounded ( if the problem says compounded quarterly, then C=4)
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
shouldn't the answer be 10000(1+x/100)?

question says that simple interest is x percent for n years. As I see it, rate is x percent per total number of years, not x percent per 1 year, so we shall not nultiply rate by n.

So, total sum =10000(1+x/100)
Amount of interest = 10000(1 + x/100) - 10000 = 10000( 1 + x/100 - 1) = 10000(1+x/100).

is wording of this particular question wordy or am I wrong in comprehension?
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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alexeykaplin wrote:
shouldn't the answer be 10000(1+x/100)?

question says that simple interest is x percent for n years. As I see it, rate is x percent per total number of years, not x percent per 1 year, so we shall not nultiply rate by n.

So, total sum =10000(1+x/100)
Amount of interest = 10000(1 + x/100) - 10000 = 10000( 1 + x/100 - 1) = 10000(1+x/100).

is wording of this particular question wordy or am I wrong in comprehension?


No. You are over analysing the question. Couple of things:

1, This is a GMATPREP question and as such you should not question the wording or the solution.
2. For simple interest problems it is x% for n years and it means that for all the 'n' # of years, the rate will be constant at x%. It is not x/n % for 1 year as you are mentioning above.

Thus, the SI on 10000 $ = 10000*x*n/100.

Hope this helps.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
I got confused with this question

I think answer D is for compound interest (which i assumed)

and answer C is for simple interest because it is not compounding.


Is this reasoning correct?
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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GMATDemiGod wrote:
I got confused with this question

I think answer D is for compound interest (which i assumed)

and answer C is for simple interest because it is not compounding.


Is this reasoning correct?


In GMAT Interest questions, any compounded interest problem will specifically mention that the interest is compounded. If no such thing is mentined, then assume that it is a simple interest problem.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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GMATDemiGod wrote:
I got confused with this question

I think answer D is for compound interest (which i assumed)

and answer C is for simple interest because it is not compounding.


Is this reasoning correct?


Percentages, Interest and More

Compound Interest Problems from our Special Questions Directory.

Theory on Percent and Interest Problems

DS Percent and Interest Problems
PS Percent and Interest Problems

Hope it helps.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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A different, less elegant, yet more straightforward approach:

Forget about formulas and plug in numbers.

- Capital: $10,000
- X = assume 5%
- N = assume 1 year

Question: "Which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years?"
In other words, the answer should yield $500 (this is your target number)
Find the answer choice that yields this target number when x = 5 and n = 1.

Answer choice C is the correct answer.
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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
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I don't understand why people are even resorting to such time consuming methods as plugging numbers.

The question is simply asking simple interest earned at n years.

Simple interest formula is
SI=pnr/100

P=principal n=years
r=rate of interest

P=10,000 r=X

SI= 10,000*n* X/100

I guess most of the attempters over read and got in the GMAT trap. The "annual" word has no bearing whatsoever on the answer. The question clearly states SIMPLE INTEREST.

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Re: If $10,000 is invested at x percent simple annual interest for n years [#permalink]
Simple interest formula = PRT => Principal * Rate * time

If you treat time as a power you're essentially determining the total interest to the power of n, but you would still need to deduct the principal.
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