If $10,000 is invested at x percent simple annual interest for n years

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

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.

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.

thanks, OA is C.

missed the point that it was only asking for interest, not the TOTAL (principal + interest)

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.

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

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

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.

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)

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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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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Hope it helps.
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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.

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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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.