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Simple Interest Problem...

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Simple Interest Problem...

by everything's eventual » Mon Aug 20, 2012 7:37 pm
Good Day,

This seems to be an easy problem but for some reason I just cannot get the right answer..appreciate help from some the geniuses here :

If $10,000 is invested at the rate of x% simple interest for n years, which of the following represents the total amount of interest in dollars that will be earned by the 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)

OA : C

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by coolhabhi » Mon Aug 20, 2012 8:29 pm
Simple Interest = p * i * n

where:
p = principal (original amount borrowed or loaned)
i = interest rate for one period
n = number of periods

Example: You borrow $10,000 for 3 years at 5% simple annual interest.

interest = p * i * n = 10,000 * (5/100) * 3 = 1,500
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by everything's eventual » Mon Aug 20, 2012 8:40 pm
Looks Easy...this was my method :

Principal : 10,000

SI : x% per year.

After one year, principal : 10,000 + 10,000x/100 = 10,000 ( 1+ x/100)
After second year, principal : 10,000 ( 1+ x/100) + 10,000 ( 1+ x/100)* x/100
= 10,000 (1+x/100) ^2

Similarly, after 'n' years, the principal = 10,000 (1+x/100)^n

What is wrong with this approach?
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by GMATGuruNY » Mon Aug 20, 2012 8:47 pm
everything's eventual wrote:Good Day,

This seems to be an easy problem but for some reason I just cannot get the right answer..appreciate help from some the geniuses here :

If $10,000 is invested at the rate of x% simple interest for n years, which of the following represents the total amount of interest in dollars that will be earned by the 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)

OA : C
Let x=10 and n=2.
Each year, the amount of interest earned = x% of 10,000 = 10% of 10,000 = 1000.
Over 2 years, the total amount earned = 2*1000 = 2000. This is our target.

Now we plug x=10 and n=2 into the answers to see which yields our target of 2000.
Only answer choice C works:
10,000n(x/100) = 10,000*2(10/100) = 2000.

The correct answer is C.
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by everything's eventual » Mon Aug 20, 2012 9:01 pm
Hello Sir...Can we use two values for variables in the same problem( in this case x and n)? With your method it is surely much easier to solve.

Just to understand, what was wrong with my approach?

Regards.
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by GMATGuruNY » Mon Aug 20, 2012 9:46 pm
everything's eventual wrote:Hello Sir...Can we use two values for variables in the same problem( in this case x and n)? With your method it is surely much easier to solve.

Just to understand, what was wrong with my approach?

Regards.
When the answer choices contain variables, we can plug in our own numbers, regardless of the number of variables.
Type into the search bar "gmatguruny" and "this is our target" to find other problems that I've solved by plugging in numbers.

Your solution calculates the principal after the first year.
There is no reason to perform this calculation: with simple interest, the principal for each year remains the same.
Interest in the first year = (x/100)10,000.
Interest in the second year = (x/100)(10,000).
And so on.
Thus, the interest earned after n years = n(x/100)(10,000).
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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by everything's eventual » Mon Aug 20, 2012 10:16 pm
Wow...my basic understanding of the subject was wrong...thank you very much...
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