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Manager  Joined: 19 Aug 2007
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If \$10,000 is invested at x percent simple annual interest  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 59% (01:18) correct 41% (01:10) wrong based on 641 sessions

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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)
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Re: PS - Simple annual interest  [#permalink]

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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.

C

The reasoning is from the following:
The formula for simple rate of interest is F = P(1+rt) where
F = future value
P = present value
r = rate
t = time

We can substitute x for r
n for t
and 10,000 in for P

F = 10,000(1+xn)

This formula will tell you the principal (original amount invested) + interest, but we only want interest, so the "1+" portion of the formula in unecessary. -->
F = 10,000(xn)

Now, we need to get the x into terms of a percentage, so we divide x by 100 -->
F = 10,000(n * x/100)

If we move the n outisde the brackets, we get -->
F = 10,000n(x/100) --> C
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Originally posted by brokerbevo on 23 Jun 2008, 10:48.
Last edited by brokerbevo on 23 Jun 2008, 10:56, edited 4 times in total.
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Director  Joined: 23 Sep 2007
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Re: PS - Simple annual interest  [#permalink]

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2
C

I = P R T

The tricky part is to recognize x/100 is the rate.

GMAT people love this particular nomenclature for some reason. When they say "x percent" they want the math to be express as x/100. For most of us (me at least), When I see x percent (ex: 50 percent), I see .5 and see no need to express it as .5/100. I have countless wrong answers due to this 1 technicality.
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Re: PS - Simple annual interest  [#permalink]

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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.

Quote:
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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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Manager  Joined: 19 Aug 2007
Posts: 180
Re: PS - Simple annual interest  [#permalink]

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thanks, OA is C.

missed the point that it was only asking for interest, not the TOTAL (principal + interest)
Intern  Joined: 10 Jan 2008
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Re: PS - Simple annual interest  [#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: I know this problem may seem easy to the business savy  [#permalink]

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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  [#permalink]

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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.

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Re: If \$10,000 is invested at x percent simple annual interest  [#permalink]

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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.

That's the compound interest formula
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Re: If \$10,000 is invested at x percent simple annual interest  [#permalink]

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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  [#permalink]

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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  [#permalink]

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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.

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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If \$10,000 is invested at x percent simple annual interest  [#permalink]

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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  [#permalink]

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alexeykaplin wrote:

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  [#permalink]

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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  [#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  [#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  [#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.

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Re: If \$10,000 is invested at x percent simple annual interest  [#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  [#permalink]

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Straight plug-in into the formula of Simple Interest.

Definitely not a 700 level question. In fact, it is a sub-600 level question. Re: If \$10,000 is invested at x percent simple annual interest   [#permalink] 06 Feb 2019, 04:39
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