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FDP question bank #3

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maolivie
 Post subject: FDP question bank #3
 Post Posted: Wed Jul 25, 2007 11:07 pm 
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?

$1500
$1750
$2000
$2500
$3000

according to the explanation:

You can solve this problem without using compound interest. 8% interest over half a year, however that interest is compounded, is approximately 4% interest. So, to compute the principal, it's actually a very simple calculation:

100 = .04x
2500 = x

The correct answer is D.

what happened to the addition of 1 in the compounding interest equation. Shouldn't it be 1.04x=100?
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Guest
 Post subject:
 Post Posted: Thu Jul 26, 2007 1:02 pm 
hi
i don't know where you got your eqn from, but the eqn for interest is: i = Prt.

100 = P(.04)(1)
P = 10,000/4
P = 2500

hope that helps!
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dbernst
 Post subject:
 Post Posted: Thu Jul 26, 2007 3:25 pm 
Offline
ManhattanGMAT Staff


Posts: 304
That is correct. In this problem, the most logical approach is to use the interest formula I = (P)(r)(t), or
100 = P(.04)(1).

The greater takeaway from this problem is the use of the word "approximately." When a problem on the GMAT specifically states "approximately," the test makers are telling you there is no reason to solve using an exact but lengthy process. Instead, use skills such as rounding, ballparking, and strategic guessing to quickly eliminate the four incorrect answer choices.

-Dan
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kramacha1979
 Post subject: Re: FDP question bank #3
 Post Posted: Wed Jun 08, 2011 10:53 pm 
Offline
Students


Posts: 69
Can someone help me solve the problem using the traditional Compound Interest formula

A = P( 1+ r/100) ^ nt

A = X+ 100
P = X

R = 8
N = 4
T = 0.5.

I don't get P = X = 2500. What am I doing wrong?
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jnelson0612
 Post subject: Re: FDP question bank #3
 Post Posted: Sat Jun 25, 2011 1:45 pm 
Offline
ManhattanGMAT Staff


Posts: 1857
kramacha1979 wrote:
Can someone help me solve the problem using the traditional Compound Interest formula

A = P( 1+ r/100) ^ nt

A = X+ 100
P = X

R = 8
N = 4
T = 0.5.

I don't get P = X = 2500. What am I doing wrong?


I think something is wrong with your formula. For example, if I have invested $100 and am getting 8 percent interest, compounded quarterly, for one year, the principal and interest at the end of the year should be about $109-$110. If I use your formula I get 100(1.08)^4. That would equal $136.04. It should actually be 1.02 that is taken to the 4th power (and of course divided by 2). Please verify your formula.

_________________
Jamie Nelson
ManhattanGMAT Instructor
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